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TABLE OF CONTENTS

Declaration

Certificate by Guide

Acknowledgement

Executive Summary

INTRODUCTION

1 Introduction to derivatives 9

2 Introduction to Forward and Futures 11

2.1 Introduction to Forward contracts 11

2.2 Introduction to Futures 11

2.3 Distinction between futures and forwards 11

2.4 Futures Prices 12

2.4.1 Cost-of-carry model in perfect markets 12

2.4.2 The reverse cash-and-carry 14

2.4.6 Payoff for derivatives contracts 19

2.4.6.1 Payoff for a buyer of Nifty futures 20

2.4.6.2 Payoff for a seller of Nifty futures 20

INDUSTRY PROFILE

History of commodity markets in India 21

present commodity market in India 21

3 Hedging Strategies 23

3.1 Face Value Naive Model 23

3.2 Market Value Naive Model 23

3.3 Conversion Factor Model 23

3.4 Basis Point Model 233.5 Regression Model 23

3.6 Price Sensitivity Model 23

4 Interest Rate Futures 24

4.1 Treasury-Bill Futures 25

4.2 Eurodollar Futures 27

4.3 Long term Treasury Futures 30

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5 Currency Futures 32

5.1 Currency Exchange Risk 30

5.2 Currency Future with example 31

5.3 Three Theories of Exchange Rate 32

5.3.1 Purchase Power Parity (PPP) 35

5.3.2 International Fisher Effect (IFE) 355.3.3 Purchasing Power Parity and Exchange Rate 36

Determination

5.3.4 Interest Rate Parity 37

5.3.5 IRP and Covered Interest Arbitrage 37

5.3.6 IRP and Hedging Currency Risk 38

5.3.7 IRP and a Forward Market Hedge 39

6 Options 40

6.1 Introduction 40

6.2 Option Terminology 41

6.3 The Four Basic Option Trades 42

6.3.1 Long Call 43

6.3.2 Long Put 44

6.3.3 Short Call ( Naked short call) 44

6.3.4 Short Put 45

6.4 Introduction to Option Strategies 46

6.5 Black Scholes Option Model 47

7 Interest Rate Derivatives 50

7.2 Points of Interest: What Determines interest Rates? 51

7.2.1 Supply and Demand 51

7.2.2 Expected Inflation 52

7.2.3 Economic conditions 53

7.2.4 Federal Reserve Actions 53

7.2.5 Fiscal Policy 54

7.3 Interest Rate Predictions 40

7.4 Forward rate agreement (FRA) 40

8 Interest rate options 55

8.1 Hedging Pre-Issue Pricing Risk for Fixed-Rate Debt 56

8.2 Hedging Solutions 57

8.2.1 Caps-Hedging against rising interest rate 58

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8.2.2 Floors-Hedging against falling interest rate 58

8.2.3 Treasury collars 58

8.3 Hedging A Large Debt Issue 59

8.4 Options on interest rate futures 60

8.5 Futures positions after option exercise. 61

8.6 Trading Example: Hedging with Options on CME Interest 62

Rate Futures 62

9 Currency Options 63

9.1 Introduction 64

9.2 Hedging with Options 67

10 Swaps 69

10.1 Introduction 70

10.2 Interest Rate Swap 70

10.3

Manage interest rate risk with a solution tailored to match a specific riskprofile 71

10.4 Why Use Swaps? 72

10.5 Interest Rate Swaps 72

10.6 An IRS can also be used to transform assets 73

10.7 Swaps for a comparative advantage 74

10.8 Swaps for Reducing the Cost of Borrowing 75

10.9 Currency Swaps 76

10.1 A plain vanilla foreign currency swap 7710.11 Station 78

11 RESEARCH DESIGN 81

12 Analysis and Interpretation 82

13 Findings 107

14 Conclusion 112

15 Annexures 115

16 Bibliography 120

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Table Of Graphs.

Figno. . Pg no.

1 Depicts the ways in which Banks/Firms have hedged 75

there interest rates.

2 Depicts the counterparty risk faced by banks/firms 75

3 Depicts the reasons for the thin trade in the Indian Interest 76

rate futures market.

4 Depicts that number of contracts has been increased due to 77

the CCILs proposal to settle FRA and I$

5 Depicts the different strategy used by the Banks and 77

Corporate to Hedge the interest rate risk.

6 Depicts the various methods used by the Banks and 78

Corporate to reduce the duration of Portfolio/BalanceSheet

7 Depicts the favourable reasons given by respondents to 78

enter with forwards than futures.

8 Depicts arbitrage opportunity exist with option pricing but 79

due to the transaction cost this disappears

9 Depicts the various variables the respondents look at while 79trading in Option.

10 Depicts the basis points which the respondent expects 80

above the term structure of interest rate because it does not

accommodate tax status, default risk, call option and

liquidity risk

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11 Depicts option adjusted spread will accommodate the risks 80

which term structure does not consider.

12 Depicts the responses given by respondents when they 81

asked about if they would like to lend and borrow 6

months down the line.

13 Depicts the various features which force the respondents to 81

enter into swaps.

14 Comparison between to Interest rate swaps currency 82

swaps.

15 Depicts the factors which influence pricing the swaps. 82

16 Depicts the various derivative products used by the banks 83

and corporate to hedge the risks like default risk, basis risk,

mismatch risk and interest rate risk.

17 Depicts most of the respondents agree that swaps are 83

superior to interest rate futures and options.

18 Depicts swap dealers enter into Interest rate futures and 84

options which has created more liquidity in bond markets.

19 Depicts the favourable reasons for the investors 84

preference to purchase structured notes.

20 Depicts the favourable reasons for the issuers to issue 85

structured notes.

21 Depicts the features available in the interest rate swaps 85which the respondents ranked according to there

preference.

22 Depicts the features available in the currency swaps which 86

the respondents ranked according to there preference

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23 Depicts that 100% respondent banks and firms trade in 86

foreign exchange.

24 Depicts the various type of arbitrage opportunity the 87

bank/firms come across when they trade in foreign

currency.

25 Depicts the exchange rate systems which the respondents 88

Liked

26 Depicts the factors which are important in determining the 88

exchange rate.

27 Depicts does FDIs and FIIs should be allowed to hedge 89

there foreign exchange in India.

28 Depicts does inflows will increase if FIIs and FDIs are 89

allowed to hedge there foreign exchange in India

29a Depicts the various reasons for the currency risk which is 90

most un hedged risk in India.

29

b Depicts the various reasons for the currency risk which is90

most un hedged risk in India.

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Executive Summary

Derivatives are one of the instruments in the hands of the investors which are useful in fulfilling

the needs of investors This can be either to hedge the risk of the underlying or to take aspeculative view and make profits or losses and arbitrage opportunities. This entirely speaks about

the derivatives, its uses and the ways how the individuals, banks and corporate use this instrument

to make huge profit. To make huge profit they want to take same amount of risk.

The topic of dissertation is Study on Forex and Debt market derivatives. This study entirely

speaks about the ways in which the interest rate risk is hedged like interest rate futures, interest

rate options, forward rate agreements and swaps, the reasons for fluctuation in interest rates, the

hedge ratio that is to be used and different ways of calculating the hedge ratio like Market Value

Nave model, Face value Nave model, Hedge Ratio, Regression Model, price sensitivity model

and others

Further the study carries towards the introduction of options, the ways how the options are helpful

in hedging the risk so that the profit is also reaped with less loss which occurs by paying

premium. The strategies used in the options like straddle, strangle, bull spread, bear spread, and

butterfly spread. It further carries towards the Black Scholes Model and the assumption made by

him for calculating the prices of the options and it also speaks regarding the Delta, Gamma, Vega,

RHO and Theta.

Then the study explains about the currency risk which is faced by most of the exporters,

importers and to those who deal in forex market and it gives a solution how the currency risk can

be hedged by using the currency futures and currency options. The factors which play the major

role in determining exchange rate and the three important theories on exchange rate i.e., Interest

rate parity, Purchase power parity and Fishers theory.

Swaps, which are more efficient than interest rate futures, currency futures, interest rate options

and currency options. The various swaps used by the individual, banks and corporate to hedge the

interest rate risk and currency risks and the use of interest rate swaps and currency swaps to

corporate.

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For most of the explanation there is a real life example how the interest rate futures and currency

futures are traded in Chicago Mercantile Exchange. Based on the study there are two questioners

for two different risks that is interest rate risk and currency risk. This questioner speaks about the

Indias position in interest rates futures and options and currency rate futures and options.

At last with findings with the reasons as to why interest rate futures thinly traded in India and

reasons as to why the currency risk is the most unhedged risk in India. And at the same time the

conclusion which talks about the steps to be taken by the RBI and SEBI in respect how to increase

the trading in Interest rate futures and options and currency futures and options.

1 . Introduction to derivatives

A derivative is a financial instrument which derives its value from some other financial price.

This other financial price is called the underlying. A wheat farmer may wish to contract to sell his

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harvest at a future date to eliminate the risk of a change in prices by that date. The price for such a

contract would obviously depend upon the current spot price of wheat. Such a transaction could

take place on a wheat forward market. The emergence of the market for derivative products,

most notably forwards, futures and options, can be traced back to the willingness of risk-

averse economic agents to guard themselves against uncertainties arising out of fluctuations

in asset prices. By their very nature, the financial markets are marked by a very high degree of

volatility. Through the use of derivative products, it is possible to partially or fully transfer price

risks by locking - in asset prices. As instruments of risk management, these generally do not

influence the fluctuations in the underlying asset prices. However, by locking- in asset prices,

derivative products minimize the impact of fluctuations in asset prices on the profitability and

cash flow situation of risk-averse investment

Derivative products initially emerged as hedging devices against fluctuations in commodity

prices, and commodity-linked derivatives remained the sole form of such products for almost

three hundred yea$ Financial derivatives came into spotlight in the post-1970 period due to

growing instability in the financial markets. However, since their emergence, these products

have become very popular and by 1990s, they accounted for about two-thirds of total

transactions in derivative products. In recent years, the market for financial derivatives has

grown tremendously in terms of variety of instruments available, their complexity and also

turnover. In the class of equity derivatives the world over, futures and options on stock

indices have gained more popularity than on individual stocks, especially among institutional

investors, who are major users of index-linked derivatives. Even small investors find these

useful due to high correlation of the popular indexes with various portfolios and ease of

use. The lower costs associated with index derivatives vis-a-vis derivative products based on

individual securities is another reason for their growing use.

1.1 Products: Forwards, Futures, Options and Swaps.

1.2 Participants: Hedgers, Speculators, and Arbitrageurs

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1.3 Functions

1. Prices in an organized derivatives market reflect the perception of markets participants

about the future and lead the prices of underlying to the perceived future level. The prices

of derivatives converge with the prices of the underlying at the expiration of the derivative

contract. Thus derivatives help in discovery of future as well as current prices.

2. The derivatives market helps to transfer risks from those who have them but may not like them

to those who have an appetite for them.

3. Derivatives, due to their inherent nature, are linked to the underlying cash markets.

With the introduction of derivatives, the underlying market witnesses higher trading

volumes because of participation by more players who would not otherwise participate for

lack of an arrangement to transfer risk.

4. Speculative trades shift to a more controlled environment of derivatives market. In the

absence of an organized derivatives market, speculators trade in the underlying cash

markets. Margining, monitoring and surveillance of the activities of various participants

become extremely difficult in these kinds of mixed markets.

5. An important incidental benefit that flows from derivatives trading is that it acts as a catalyst

for new entrepreneurial activity. The derivatives have a history of attracting many bright,

creative, well-educated people with an entrepreneurial attitude. They often energize others

to create new businesses, new products and new employment opportunities, the benefit of

which are immense

6. Derivatives markets help increase savings and investment in the long run. Transfer of risk

enables market participants to expand their volume of activity.

2. Introduction to Forward and Futures

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2.1 Introduction to Forward contracts

In a forward contract, two parties irrevocably agree to settle a trade at a future date, for a stated

price and quantity. No money changes hands at the time the trade is agreed upon.

Suppose a buyer L and a seller S agrees to do a trade in 100 grams of gold on 31 Dec 2005 at

$5, 000/ten gram. Here, $5, 000/tola is the forward price of 31 dec 2005 gold.

The buyer L is said to be long and the seller S is said to be short. Once the contract has been

entered into, L is obligated to pay S $ 500,000 on 31 Dec 2005, and take delivery of 100 gram of

gold. Similarly, S is obligated to be ready to accept $500, 000 on 31 Dec 2005, and give 100 gram

of gold in exchange.

2.2 Introduction to Futures

A futures contract is an agreement between two parties to buy or sell an asset at a

certain time in the future at a certain price. Futures contract is same as forward contracts.

But unlike forward contracts, the futures contracts are standardized and exchange traded.

2.3. Distinction between futures and forwards

Futures Forwards

Trade on an organized exchange OTC in nature

Standardized contract terms Customised contract

terms

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2.4 Futures Prices

2.4.1 Cost-of-carry model in perfect markets

Assume that markets are perfect in the sense of being free from transaction costs and

restrictions on short selling. The spot price of gold is $370. Current interest rates are 10

percent per year, compounded monthly. According to the cost-of-carry model, the price of a

gold futures contract be if expiration is six months away is In perfect markets, the cost-of-carry

model gives the futures price as:

F0,t = S0 (1 +C)

F0,t = the future price at t=0 for delivery at t=1

S0 = the spot price at time t=0

C = the cost of carry, expressed as a fraction of the spot price, necessary to carry the good

forward from the present to the delivery date on the futures.

The cost of carrying gold for six months is (1+.10/12)6- 1= .051053. Therefore, the futures

price should be: F0, t = $370(1.051053) = $388.89

2.4.2 Consider the information of 2.4.1 given above.

Now let us assume that futures trading costs are $25 per 100-ounce gold contract, and buying

Hence more liquid Hence less liquid

Requires margin payments No margin payment

Follows daily settlement Settlement happens at

end of period

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or selling an ounce of gold incurs transaction costs of $1.25. Gold can be stored for $.15

per month per ounce. (Ignore interest on the storage fee and the transaction costs.) What futures

prices are consistent with the cost-of-carry model?

Answering this question requires finding the bounds imposed by the cash-and-carry and

reverse cash-and-carry strategies. For convenience, we assume a transaction size of one 100-

ounce contract.

2.4.2.1 For the cash-and-carry, the trader buys gold and sells the futures. This

strategy requires the following cash outflows:

Borrow to finance these outlays -$37,215

Six months later, the trader must:

Pay the transaction cost on one future -$25

Repay the borrowing -$39,114.95

Deliver on futures ?

Net outlays at the outset were zero, and they were $39,139.95 at the horizon. Therefore,

the futures price must exceed $391.40 an ounce for the cash-and-carry strategy to yield a

profit.

2.4.2.2 The reverse cash-and-carry incurs the following cash flows. At the outset,

the trader must:

Transactions Cash flow

Buy gold -$370(100)

Pay transaction costs on the spot -$1.25(100)

Pay the storage cost -$.15(100) (6)

Sell futures 0

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Particulars Cash flows

Sell gold +$370(100)

Pay transaction costs on the spot -$1.25(100)

Invest funds -$36,875

Buy futures 0

These transactions provide a net zero initial cash flow. In six months, the trader has the

following cash flows:

Collect on investment +$36,875(1+.10/12)6= $38,757.59

Pay futures transaction costs -$25

Receive delivery on futures ?

The breakeven futures price is therefore $387.33 per ounce. Any lower price will generate

a profit. From the cash-and-carry strategy, the futures price must be less than $391.40 to prevent

arbitrage. From the reverse cash-and-carry strategy, the price must be at least $387.33. (Note

that we assume there are no expenses associated with making or taking delivery.)

2.4.3 Consider the information given in 2.4.1 and 2.4.2 above.

Restrictions on short selling effectively mean that the reverse cash-and-carry trader in the

gold market receives the use of only 90 percent of the value of the gold that is sold short. Based

on this new information, what is the permissible range of futures prices? This new assumption

does not affect the cash-and-carry strategy, but it does limit the profitability of the reverse

cash-and-carry trade. Specifically, the trader sells 100 ounces short but realizes only

.9($370)(100) =$33,300 of usable funds. After paying the $125 spot transaction cost, the trader

has $33,175 to invest. Therefore, the investment proceeds at the horizon are:

$33,175(1+.10/12)6= $34,868.69.

Thus, all of the cash flows are:

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Sell gold +$370(100)

Pay transaction costs on the spot -$1.25(100)

Broker retains 10 percent -$3,700

Invest funds -$33,175

Buy futures 0

These transactions provide a net zero initial cash flow. In six months, the trader has the

following cash flows:

Collect on investment $34,868.69

Receive return of deposit from broker $3,700

Pay futures transaction costs $25

Receive delivery on futures ?

The breakeven futures price is therefore $385.44 per ounce. Any lower price will generate

a profit. Thus, the no-arbitrage condition will be fulfilled if the futures price equals or exceeds

$385.44 and equals or is less than $391.40.

2.4.4 Consider all of the information about gold from 2.4.1 to 2.4.3 . The interest

rate in question 2.4.1 is 10 percent per annum, with monthly compounding. This is the

borrowing rate. Lending brings only 8 percent, compounded monthly. What is the

permissible range of futures prices when we consider this imperfection as well?

The lower lending rate reduces the proceeds from the reverse cash-and-carry strategy.

Now the trader has the following cash flows:

Transactions Cash

flow

Sell gold

+$370(100)

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Pay transaction costs on the spot -

$1.25(100)

Broker retains 10 percent -

$3,700

Invest funds -

$33,175

Buy futures 0

These transactions provide a net zero initial cash flow. Now the investment will yield only

$33,175(1+.08/12)6= $34,524.31.

In six months, the trader has the following cash flows:

Total proceeds on the 100 ounces are $38,199.31. Therefore, the futures price per ounce

must be less than $381.99 for the reverse cash-and-carry strategy to profit. Because the

borrowing rate has not changed, the bound from the cash-and-carry strategy remains at

$391.40. Therefore, the futures price must remain within the inclusive bounds of $381.99 to

$391.40 to exclude arbitrage.

2.4.5 Consider all of the information about gold from 2.4.1 to 2.4.4 .

The gold future expiring in six months trades for $375 per ounce. Given all of the

market imperfections we have considered assuming that gold trades for $395.

If the futures price is $395, it exceeds the bound imposed by the cash-and-carry strategy,

Transactions Cash flow

Collect on investment $34,524.31

Pay futures transaction costs $25

Receive delivery on futures ?

Return gold to close short sale 0

Receive return of deposit from broker $ 3,700

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and it should be possible to trade as follows:

Cash-and-Carry Arbitrage

t = 0

Borrow $37,215 for 6 months at 10%. +$37,215.00

Buy 100 ounces of spot gold. -37,000.00

Pay storage costs for 6 months. -90.00

Pay transaction costs on gold purchase. -125.00

Sell futures for $395. 0.00

Total Cash Flow $0

t = 6

Remove gold from storage. $0

Deliver gold on futures. +39,500.00

Pay futures transaction cost. -25.00

Repay debt. -39,114.95

Total Cash Flow -$360.05

If the futures price is $375, the reverse cash-and-carry strategy should generate a profit as

follows:

Reverse Cash-and-Carry Arbitrage

t= 0

Sell 100 ounces of gold short. +$37,000.00

Pay transaction costs. -125.00

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t= 6

Collect on investment. -$34,524.31

Receive delivery on futures. -37,500.00

Return gold to close short sale. 0

Receive return of deposit from broker. +3,700.00

Pay futures transaction cost. -25.00

Total Cash Flow +$699.31

2.4.6 Payoff for derivatives contracts

2.4.6.1 Payoff for a buyer of Nifty futures

The figure shows the profits/losses for a long futures position. The investor bought futures

when the index was at 1220. If the index goes up, his futures position starts making profit.

If the index falls, his futures position starts showing losses.

Broker retains 10%. -3,700.00

Buy futures. 0

Invest remaining funds for 6 months at 8%. -33,175.00

Total Cash Flow $0

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2.4.6.2 Payoff for a seller of Nifty futures

The figure shows the profits/losses for a short futures position. The investor sold

futures when the index was at 1220. If the index goes down, his futures position starts

making profit. If the index rises, his futures position starts showing losses.

Industry Profile.

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History of Commodity markets in India.

The history of organized commodity derivatives in India goes back to the 19 th century when

Cotton Trade Association started futures trading in 1875, about a decade after they started inChicago. Over the time derivatives market developed in several commodities in India. Following

Cotton derivatives trading started in oilseed in Bombay (1900), raw jute and jute goods in

Calcutta(1912), Wheat in Hapur (1913) and bullion in Bombay (1920).

However many feared that derivatives fuelled unnecessary speculation and were detrimental to

the healthy functioning of the market for the underlying commodities, resulting in to banning of

commodity options trading and cash settlement of commodities futures after independence in1952. The parliament passed the forward contracts (regulation) act, 1952, which regulated

contracts in Commodities all over the India. The act prohibited options trading in goods along

with cash settlement of forward trades, rendering a crushing blow to the commodity derivatives

market. Under the act only those associations/exchanges which are granted reorganizations from

the government are allowed to organize forward trading in regulated commodities.

The act envisages three tier regulations :

1. Exchange which organizes forward trading in commodities can regulate trading on day to

day basis.

2. Forward market commission provides regulatory oversight under the powers delegated to

it by the central government.

3. The central governmentdepartment of consumer affairs, ministry of consumer affairs,

food and public distribution- is the ultimate regulatory authority.

After Liberization and Globalization in 1990, the government set up a committee (1993) to

examine the role of futures trading in 17 commodity groups. It also recommended strengthening

Forward Markets Commisions, And certain amendments to Forward Contracts (regulation) Act

1952, particularly allowing option trading in goods and registration of brokers with forward

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Market Commision. The government accepted most of these recommendations and future trading

was permitted in all recommended commodities. It is timely decision since internationally the

commodity cycle is on upswing and the next decade being touched as the decade of commodities.

Commodity exchange in India plays an important role where the prices of any commodity are not

fixed in an organized way.

PRESENT COMMODITY MARKET IN INDIA.

Today , commodity exchanges are purely speculative in nature. Before discovering the price ,

they reach to the producers, end users, and even the retail investors, at a grass roots level. It brings

a price transparency and risk management in the vital market. By Exchanging rules and by law,

no one can bid under a higher bid, and no one can offer to sell higher than someone elses lower

offer. That keeps the market as efficient as possible and keeps the traders on their toes to make

sure no one gets the purchase or sale before they do. Since 2002, the commodities future market

in India has experienced an unexpected boom in terms of modern exchanges, number of

commodities allowed for derivatives trading as well as the value of futures trading in commodities

which crossed $ 1trillion mark in 2006.

In India there are 25 recognized future exchanges of which there are four national level multi

commodity exchanges. After a gap of almost three decades, government of India has allowed

forward transactions in commodities through Online Commodity Exchanges, a modification of

traditional business known as Adhat and Vayda Vyapar to facilitate better risk coverage and

delivery of commodities.

The four Exchanges are :

a. National Commodity & Derivatives Exchange Limited (NCDEX) Mumbai.

b. Multi Commodity Exchange of India Limited (MCX) Mumbai and

c. National Multi-commodity Exchange of India Limited (NMCEIL) Ahmedabad.

d. Indian Commodity Exchange Limited(ICEX), Gurgaon.

3. Hedging Strategies

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Alex Brown has to hedge $500 million of long-term debt that his firm plans to issue in May. The

possible strategies Alex Brown could use to hedge his impending debt issue.

3.1 Face Value Naive Model: In this method Alex would trade one dollar of nominal futures

contract per one dollar of debt face value. The major benefit of this method is the ease of

implementation. Unfortunately, it ignores market values and the differential responses of the

bond and futures contract prices to interest rates.

3.2 Market Value Naive Model: In this method Alex would hedge one dollar of debt market

value using one dollar of futures price value. That is, the hedge ratio is determined by the

market prices instead of nominal and face values. Unfortunately, it does not consider the price

sensitivities of the two instruments.

3.3 Conversion Factor Model: This model can be used when the hedging instrument is a T-

note or T-bond futures contract. The conversion factor adjusts the prices of deliverable

bonds and notes that do not have a 6% coupon to make them equivalent to the 6% coupon

bond or note that is called for in the contract. The hedge ratio is determined by

multiplying the Face Value Naive hedge ratio by the conversion factor. The appropriate

conversion factor to use is the conversion factor of the cheapest to deliver T-bond or T-

note. This model still ignores price sensitivity differences between the hedging and hedged

instruments. The hedge ratio is calculated as below.

HR= - (Cash market principal/Futures market principal)*(Conversion

Factor)

3.4 Basis Point Model: This model uses the price changes of the futures and cash

positions resulting from a one basis point change in yields to determine the hedge ratio. It

is calculated as:

HR = - BPCs/BPCf

This model works well if the cash and futures instruments face the same rate volatility. If

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they face different volatilities and that relationship can be quantified, then the basis point model

can be adjusted to account for the differing volatilities.

3.5 Regression Model: In the regression model the historic relationship between cash market

price changes and futures market price changes is estimated. This estimation is accomplished by

regressing price changes in the cash market on futures price changes. The slope coefficient

from this regression is then used as the hedge ratio.

Alex may not find this model useful, as he is trying to hedge a new debt issue. Even if Alex had

an historic price stream on 30-year corporate debt issues, the historic relationship with the

futures price might prove to be an unreliable indicator of the present or future relationship.

This stems from the fact that the price response of the futures contract is determined by the

cheapest-to-deliver bond. The cheapest-to-deliver bond can vary in maturity from 15 years

to 30 yea$ This means that the futures contract can have very different price responses to

interest rates at different points in time.

For the RGR model the hedge ratio is:

HR= - (COVs,f/Variance of futures)

COVs,f = covariance between cash and futures.

3.6 Price Sensitivity Model : This may be a good model for Alex to use. It is designed for

interest rate hedging, and it accounts for the differential price responses of the hedging and

the hedged instruments. The model is duration-based so that it accounts for maturity and

coupon rate differences of the cash and the futures positions. It is computed as:

N= - (Pi MDi/FPfMDF)RYC

Where:

FPF and Pi are the respective futures contract and cash instrument prices; MDi and

MDF are the modified durations for the cash and futures instruments, respectively, and

RYC is the change in the cash market yield relative to the change in the futures yield.

Let us look at an example . Alex Brown has just returned from a seminar on using

futures for hedging purposes. As a result of what he has learned, he re-examines his

decision to hedge $500 million of long-term debt that his firm plans to issue in May.

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Face Value Naive hedge: In this model Alex current hedge is a short position of 5,000

T-bond futures contracts ($100,000 each). Currently Alex has employed a Face Value Naive

hedge. For each dollar of debt principal he plans to issue, he is short $1 of nominal T-bond

futures. The benefit of the strategy is its ease of implementation. The drawback is that cash

instrument and the T-bond futures may have differential price responses to interest rate

changes.

Price sensitivity hedge: Alex feels that a price sensitivity hedge would be most

appropriate for his situation. The additional information is if the debt could be issued today, it

would be priced at 119-22 to yield 6.5%. With its 8% coupon and 30 years to maturity, the

duration of the debt would be 13.09 yea$ On the futures side, the futures prices are based

on the cheapest-to-deliver bonds, which are trading at 124-14 to yield 5.6%. These bonds have

duration of 9.64 yea$

The price sensitivity hedge ratio is:

FPF = 124.4375%*0.1 million MDF = 9.128788

Pi = 119.6875%_500 million MDi = 12.29108

To hedge the risk, 6,475 contracts should be sold.

4. Interest Rate Futures

Interest rate futures were introduced in 1975 and were an immediate success. The volume

represents about one half of all future market activity. Almost all of the trading in interest rate

futures is at the Chicago Board of Trade and the International Money Market (IMM) of the

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Chicago Mercantile Exchange.

4.1 Treasury-Bill Futures

The IMM T-Bill contract calls for the delivery of treasury bills with a face value of $1 million and

90 days to maturity at the expiration of the contract. The IMM uses a special code for stating the

price of T-bills; i.e., the price is given by the IMM index which is 100-DY, where DY is the

discount yield in percent. An alternative way of stating this relation for bills having a year until

maturity is:

PRICE OF CONTRACT = 1,000,000(1 - DY/100)

If the T-bills have DTM days to maturity the price is given by:

PRICE OF CONTRACT = 1,000,000(1 - (DY/100)(DTM/360))

For every change in the discount yield of one basis point (1/100 of 1 percent) the price of the

contract changes by $25.

The price of a $1,000,000 face value 90-day T-bill has a discount yield of 8.75

percent. Applying the equation for the value of a T-bill, the price of a $1,000,000 face value T-bill

is $1,000,000 -DY($1,000,000)(DTM)/360, where DY is the discount yield and DTM= days until

maturity. Therefore, if DY=0.0875 the bill price is:

Bill Price= $1,000,000-{(0.0875 ($1,000,000) (90))/360} = $978,125

Let us look at one more example. The IMM Index stands as 88.70. If you buy a T-bill future at

that index value and the index becomes 88.90, what is your gain or loss? The discount yield =

100.00- IMM Index = 100.00- 88.70 = 11.30 percent. If the IMM Index moves to 88.90, it has

gained 20 basis points, and each point is worth $25. Because the price has risen and the yield has

fallen, the long position has a profit of $25(20) = $500.

4.2 Eurodollar Futures

Eurodollars are any dollar denominated deposit in a bank outside of the U.S. Thus dollar deposits

in Singapore are still called Eurodollars Eurodollar accounts are not transferable but banks can

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lend on the basis of the Eurodollar accounts it holds. The interest rate charged for Eurodollar

loans is often based upon the London Inter bank Offer Rate (LIBOR).

The Eurodollar contract on the IMM is also for $1 million. Since Eurodollar accounts are not

transferable it is not possible to actually make delivery on Eurodollar contracts. Instead there is a

cash settlement at the end of the contract period. In the case of Eurodollar contracts the discount

yield is replaced by an add-on yield which is the interest earned in proportion to the original price.

Thus,

Add-on Yield = DY/(1 - DY/100)

CME Eurodollar Interest Rate Futures Example

Suppose a financial manager of a company wishes to borrow US$10 million for 1 year at a fixed

rate. She can ask a bank for a fixed rate for 1 year directly or a floating rate and seek to hedge

using an interest rate futures (eg: the CME Eurodollar futures).

The value of a CME Eurodollar interest rate futures contract rises when interest rates fall and vice

versa, hence the manager would need a short position to hedge. Hence if interest rates rise, the

value of the contract falls and a short position is in the money (sold high, can buy back low).

The notional principal of a CME Eurodollar interest rate futures contract is US$1million. The

price of the CME Eurodollar interest rate futures contract at the maturity date is 100- R where R

is the 90-day Libor interest rate that starts when the contract matures on the 3rd Wednesday or

each delivery month. This interest rate is then the underlying variable for this contract.

The value of the CME Eurodollar interest rate futures contract on any given day

before it matures is given by the formula: 10000*[100-0.25(100-Z)] where Z is the price of the

futures contract at that time - given by supply and demand! This implies that for each basis point

move in the price, the contract value changes by US$25.

E.g.: If Z = 94.32, V = 985,800

If Z = 94.33, V = 985,825

The contract is settled daily like any futures contract with variation margin payments. Suppose the

company does not hedge and interest rates and interest payments (using 90/360 convention) turn

out to be:

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Sep 15 1.89% 47250

Dec 15 2.44% 61000

Mar 15 2.75% 68750

Jun 15 2.90% 72500

Total interest rate cost = 249500

Suppose the financial manager hedges by selling US$10 million CME Eurodollar interest rate

futures short for maturities Sep, Dec and Mar and the relevant prices are as follows:

Prices at Maturity

This implies

VToday/Sep=10*10000*[100-0.25(100-97.92)]=9948000

VSep/Sep= 10*10000*[100-0.25(100-97.60)]=9940000

Profit = 8000 = 10*25*(9792-9760)

VToday/Dec=10*10000*[100-0.25(100-97.46)]=9936500

VDec/Dec= 10*10000*[100-0.25(100-97.31)]=9932750

Profit = 3750 = 10*25*(9746-9731)

VToday/Mar=10*10000*[100-0.25(100-96.82)]=9920500

VMar/Mar= 10*10000*[100-0.25(100-97.15)]=9932750

Profit = -8250 = 10*25*(9682-9715)

Today Sep Dec

Mar

Spot 1.89%

Futs Sep 2.08% (97.92) 97.60 (2.4%)

Dec 2.54% (97.46) 97.31 (2.69%)

Mar 3.18% (96.82)

97.15 (2.85%)

Total costs

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Total costs 249500-3500 = 246000

4.3 Long term Treasury Futures

Regardless of your market outlook, U.S. Treasury bond and note futures are the ideal tools to help

you adjust the risk/return characteristics of your fixed income securities. Here are some of the

many risk-management opportunities they offer.

Lock in a Purchase Price: If you plan to purchase fixed-income securities in the futures and are

concerned about the possibility of higher prices, you can buy Treasury futures and secure a

maximum purchase price.

Preserve Investment Value: By selling Treasury futures, you can lock in an attractive selling price

and protect the value of a portfolio or individual security against possible decreasing prices.

Cross-Hedge: U.S. Treasury bond and note futures can be used to control risk and enhance the

returns of non-U.S. government securities. Treasury futures can be effective risk-management

tools for corporate bonds, Eurobonds, and other fixed-income instruments.

Trade Changes in the Yield Curve

Because Treasury futures cover a wide spectrum of maturities from short-term notes to long-term

Interest costs as before Futures

profit/loss

Sep 15 1.89% 47250

Dec 15 2.44% 61000 8000

Mar 15 2.75% 68750 3750

Jun 15 2.90% 72500 -8250

Total interest rate cost 249500 3500 (profit)

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bonds, you can construct trades based on the differences in interest rate movements all along the

yield curve.

Contract Specifications:

Trading Unit

T-bond Futures - One U.S. Treasury bond with $100,000 face value at maturity.

10-year T-note Futures - One U.S. Treasury note with $100,000 face value at

maturity.

5-year T-note Futures - One U.S. Treasury note with $100,000 face value at

maturity.

2-year T-note Futures - One U.S. Treasury note with $200,000 face value at

maturity.

Deliverable Grades

T-bond Futures- Bonds with at least 15 years remaining to maturity.

10-year T-note Futures- Notes with 61/2 to 10 years remaining to maturity.

5-year T-note Futures- Notes with 4 years 3 months to 5 years 3 months remaining to

maturity.

2-year T-note Futures- Notes with 1 year 9 months to 2 years remaining to maturity.

Tick Size

T-bond Futures - 1/32

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10-year T-note Futures - 1/32

5-year T-note Futures - 1/2 of 1/32

2-year T-note Futures - 1/4 of 1/32

5. Currency Futures

5.1 Currency Exchange Risk

How do currency fluctuations affect import/exporters?

Exchange rate volatility can work against an international company if a payment in a foreign

currency has to be made at a future date. There is no way to guarantee that the price in the

currency market will be the same in the future-it is possible that the price will move against the

company, making the payment cost more. On the other hand, the market can also move in a

business' favour, making the payment cost less in terms of their home currency. Generally, firms

that export goods to other countries benefit when their home currency depreciates, since their

products become cheaper in other countries. Firms that import from other countries benefit when

their currency becomes stronger, since it enables them to purchase more.

Hedging Against Currency Risk to Avoid the Volatility Trap

so how can a business protect against a risky currency? One way is to avoid the risk by

minimizing their commercial involvement with countries that have volatile currencies like the

Japanese Yen. This is however not a practical solution. Another way is to hedge in the spot

currency market by taking a position that effectively neutralizes the volatility in the pair.

5.2 Currency Future: It is a futures contract to exchange one currency for another at a specified

date in the future at a price (exchange rate) that is fixed on the last trading date. Typically, one

of the currencies is the US dollar. The price of a future is then in terms of US dollars per unit

of other currency. This can be different from the standard way of quoting in the spot foreign

exchange markets. The trade unit of each contract is then a certain amount of other

currency, for instance EUR 125,000. Most contracts have physical delivery, so for those held

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at the end of the last trading day, actual payments are made in each currency. However,

most contracts are closed out before that.

Example

Peter buys 10 September CME Euro FX Futures, at 1.2713 USD/EUR. At the end of the day,

the futures close at 1.2784 USD/EUR. The change in price is 0.0071 USD/EUR. As each

contract is over EUR 125,000, and he has 10 contracts, his profit is USD 8,875. As with any

future, this is paid to him immediately.

More generally, each change of 0.0001 USD/EUR (the minimum tick size), is a profit or loss of

USD 12.5 per contract.

Investors use these futures contracts to hedge against foreign exchange risk. They can also be

used to speculate and, by incurring a risk, attempt to profit from rising or falling

exchange rates. Investors can close out the contract at any time prior to the contract's

delivery date.

Currency futures were first created at the Chicago Mercantile Exchange (CME) in 1972,

less than one year after the system of fixed exchange rates was abandoned along with the

gold standard. Some commodity traders at the CME did not have access to the inter-bank

exchange markets in the early seventies, when they believed that significant changes were

about to take place in the currency market. They established the International Monetary

Market (IMM) and launched trading in seven currency futures on May 16, 1972. Today, the

IMM is a division of CME. In the second quarter of 2005, an average of 332,000 contracts

with a notional value of USD 43 billion were traded every day. Most of these are traded

electronically nowadays.

A futures contract is like a forward contract it specifies that a certain currency will be exchanged

for another at a specified time in the future at prices specified today. A futures contract is

different from a forward contract. Futures are standardized contracts trading on organized

exchanges with daily resettlement through a clearinghouse .

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The Standardizing Features

Contract Size

Delivery Month

Daily resettlement

Initial Margin (about 4% of contract value, cash or T-bills held in a street name at your

brokers).

Suppose you want to speculate on a rise in the $/ exchange rate

(specifically youthink that the dollar will appreciate).think that the dollar will appreciate).

$1 = 140 and it appears that the dollar is strengthening.

-month futures contract to sell at the rate of $1 = 150

you will make money if the yen depreciates.

12,500,000

$3,333.33 =.04* 12,500,000*$1/Y150

If tomorrow, the futures rate closes at $1 = 149, then your positions value drops.

Your original agreement was to sell 12,500,000 and receive $83,333.33

But now 12,500,000 is worth $83,892.62

$ $1/149.

You have lost $559.28 overnight

The $559.28 comes out of your $3,333.33 margin account, leaving $2,774.05

This is short of the $3,355.70 required for a new position.

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$ $1/149.

Your broker will let you slide until you run through your maintenance margin Then you must post

additional funds or your position will be closed out. This is usually done with a reversing trade.

5.3 Three Theories of Exchange Rate

5.3.1Purchase Power Parity (PPP)

Focuses on inflation and exchange rate relationship if the law of one price was true for all goods

and services, we could obtain the theory of PPP. It Postulates the equilibrium exchange rate

between currencies of two countries is equal to the ratio of the price levels in the two nations.

Prices of similar products of two different countries should be equal when measured in a common

currency

For example if nation A is US and nation B is the UK the exchange rate b/w dollar and pound is

equal to the ratio of US to UK prices. If the general price level in US is twice to the general level

in UK, then the absolute PPP theory postulates equilibrium rate to be

Rab = S 2/Stg 1

5.3.2 International Fisher Effect (IFE)

IFE Uses Interest Rates rather than inflation rate difference to explain the changes in interest rates

over time. IFE is closely related to PPP because interest rates are significantly correlated with

inflation rates. The relationship b/w the percentage change in the spot exchange rates in different

national capital markets is known as IFE. IFE suggests that given two countries, the currency with

the higher interest rates will depreciate by the amount of interest rate differential. This is with a

country the nominal interest rate tends to approximately equal the real interest rate plus the

expected inflation The proportion that the nominal interest rate varies directly with the expected

inflation rate, known as Fisher effect has subsequently been incorporated into the theory of

exchange rate determination.

IRP is an arbitrage condition that must hold when international financial markets are in

equilibrium. Suppose that you have $ 1 to invest over, say a one-year period.

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Consider two alternative ways of investing your fund.

1. Invest domestically at the U.S interest rate or alternatively

2. Invest in a foreign country, say the U.K. at the foreign interest rate and hedge the

exchange risk by selling the maturity value of the foreign investment forward.

An increase (decrease) in the expected rate of inflation will cause a proportionate increase

(decrease) in the interest rate in the country.

For the U.S., the Fisher effect is written as:

i$ = $ + E($)

Where,

$ is the equilibrium expected real US interest rate.

E($) is the expected rate of U.S. inflation

i $ is the equilibrium expected nominal U.S. interest rate

If the Fisher effect holds in the U.S. i$ = $ + E($) and the Fisher effect holds in

Japan, i = + E() and if the real rates are the same in each country $ = then we get the

Interna tional Fisher Effect E(e) = i$ - i .

5.3.3 Purchasing Power Parity and Exchange Rate Determination

The exchange rate between two currencies should equal the ratio of the countries price levels.

S ($/) =P$ P

Relative PPP states that the rate of change in an exchange rate is equal to the differences in the

rates of inflation.

e = $ -

If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 3%.

The real exchange rate is

If PPP holds, (1 + e) = (1 + $)/(1 + ), then q = 1.

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Ifq < 1 competitiveness of domestic country improves with currency depreciations.

Ifq > 1 competitiveness of domestic country deteriorates with currency depreciations

5.3.4 Interest Rate Parity

IRP is an arbitrage condition. If IRP did not hold, then it would be possible for an astute trader

to make unlimited amounts of money exploiting the arbitrage opportunity. Since we dont

typically observe persistent arbitrage conditions, we can safely assume that IRP holds.

Suppose you have $100,000 to invest for one year.

You can either Invest in the U.S. at i$. Future value = $100,000(1 + ius )

1. Trade your dollars for yen at the spot rate, invest in Japan at i andhedge your exchange rate

risk by selling the future value of the Japanese investment forward. The future value =

$100,000(F/S)(1 + i) .Since both of these investments have the same risk, they must have the

same future value.otherwise an arbitrage would exist. (F/S)(1 + i) = (1 + ius) Formally, (F/S)(1

+ i) = (1 + ius) or if you prefer,IRP is sometimes approximatedas

If IRP failed to hold, an arbitrage would exist. Its easiest to see this in the form of an

example.

Consider the following set of foreign and domestic interest rates and spot and forward exchange

rates.

5.3.5 IRP and Covered Interest Arbitrage

A trader with $1,000 to invest could invest in the U.S., in one year his investment will be worth

$1,071 = $ i$) = $ Alternatively, this trader could exchange $1,000 for

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800 at the prevailing spot rate, (note that 800 = $1,000$1.25/) invest 800 at i = 11.56%

for one year to achieve 892.48. Translate 892.48 back into dollars at F360($/) = $1.20/, the

892.48 will be exactly $1,071. According to IRP only one 360-day forward rate, F360 ($/),

can exist. It must be the case that F360 ($/) = $1.20/ Why? IfF360 ($ $1.20/, an astute

trader could make money with one of the following strategies:

Arbitrage Strategy I

IfF360 ($/) > $1.20/

i. Borrow $1,000 at t= 0 at i$ = 7.1%.

ii. Exchange $1,000 for 800 at the prevailing spot rate, (Note that 800 =$1,000$1.25/)

invest 800 at 11.56% (i) for one year to achieve 892.48

iii. Translate 892.48 back into dollars, ifF360 ($/) > $1.20/ , 892.48 will be more than

enough to repay your dollar obligation of $1,071.

Arbitrage Strategy II

IfF360 ($/) < $1.20/

i. Borrow 800 at t= 0 at i= 11.56%.

ii. Exchange 800 for $1,000 at the prevailing spot rate, invest $1,000 at

7.1% for one year to achieve $1,071.

iii. Translate $1,071 back into pounds, ifF360($/) < $1.20/ , $1,071 will be more than enough

to repay your obligation of 892.48.

5.3.6 IRP and Hedging Currency Risk

You are a U.S. importer of British woolens and have just ordered next years

inventory. Payment of 100M is due in one year.

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IRP implies that there are two ways that you fix the cash outflow

a) Put your self in a position that delivers 100M in one year.a long forward

contract on the pound. You will pay (100M)(1.2/) = $120M

b) Form a forward market hedge as shown below.

5.3.7 IRP and a Forward Market Hedge

To form a forward market hedge:

Borrow $112.05 million in the U.S. (in one year you will owe $120 million).

Translate $112.05 million into pounds at the spot rate S($/) = $1.25/ to receive

89.64 million.

Invest 89.64 million in the UK at i = 11.56% for one year.

In one year your investment will have grown to 100 million.exactly enough to pay your

supplier.

Forward Market Hedge

Where do the numbers come from? We owe our supplier 100 million in one year.

so we know that we need to have an investment with a future value of 100 million.

Since i = 11.56% we need to invest 89.64 million at the start of the year.

How many dollars will it take to acquire 89.64 million at the start of the year if

S ($/) = $1.25/?

6. Options

6.1 Introduction: An option is a contract which gives its holder the right, but not the obligation,

to buy (or sell) an asset at some predetermined price within a specified period of time. An option

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is a contract which gives its holder the right, but not the obligation, to buy (or sell) an asset at

some predetermined price within a specified period of time.

A real life example

Suppose you are on your way to home one day and you notice that house at the end of the street

is for sale. Its bigger then your current house and has a double bed room. All this costs only

$100,000. You.ve just got to buy it! One problem is money: you dont have any. but within a

couple of months, you think you could get it. So what do you do? Wait and risk losing the house

to another buyer?

Here is something you could do: lets say you go down and see the owner of the house and

explain your situation. He feels for your predicament and suggests that you pay a fee of $1,000.

For that $1,000 he will hold the house for exactly two months and no longer. Should you wish to

buy it, you will have to pay $100,000. This means your total cost is $100,000 + $1,000 =

$101,000.

You.ve just bought yourself a call option!

Within the two months you can raise the money and buy the house. You could forget the deal all

together and lose the $1000, but not be liable for anything else. Note : paying the $1000 gives

you the right but not the obligation to buy the house. The owner of the house would be obliged to

sell it to you should you so desire, but only

before the two months are up.

Lets fast forward. Two months are almost up and you have managed to secure some finance.

Paying the full price for the house is not a problem. However, you have just read in the

newspaper that housing prices in your area have fallen in the last two months. Your dream house

now has a $90,000 price tag.

What do you do? Take up the option to buy it for $10,000 for more than its worth?

Certainly not! You would be happy to let your option expire, losing the $1,000 deposit. You

could however go and buy the house at the current market price of $90,000 and save the

difference.

However lets say housing prices have increased and the house is really worth $110,000. What

do you do? You would take up your option to buy at $100,000 and the seller would be obliged to

sell it to you. In the markets, this is the same as exercising a call option.

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Hey, if you were so inclined, you could then sell the house at market price and make a handsome

$9,000 profit ($110,000 - $101,000 = $9,000). Then again you might just want to live in it, but

thats beside the point.

6.2 Option Terminology

Call option: An option to buy a specified number of shares of a security within some

future period.

Put option: An option to sell a specified number of shares of a security with in some

future period.

Exercise (or strike) price: The price stated in the option contract at which the security

can be bought or sold.

Option price: The market price of the option contract.

Expiration date: The date the option matures.

Exercise value (intrinsic value): The value of a call option if it were exercised

today = Current stock price - Strike price.

Note: The exercise (intrinsic) value is zero if the stock price is less than the strike

price.

Seller of option is called Option Writer

Covered option: A call option written against stock held in an investor portfolio Naked

(uncovered) option: An option sold without the stock to back it up.

In-the-money call: A call whose exercise (strike) price is less than the current price of

the underlying stock.

Out-of-the-money call: A call option whose exercise (strike) price exceeds the current

stock price.

LEAPs: Long-term Equity Anticipation securities that are similar to conventional options

except that they are long-term options with maturities of up to 2 1/2 years

Consider the following data.

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6.3 The Four Basic Option TradesThese trades are described from the point of view of a speculator. If they are combined

with other positions, they can also be used in hedging.

6.3.1 Long Call : A trader who believes that a stock's price will increase may buy the stock or

instead, buy the right to purchase the stock (a call option). He has no obligation to buy

the stock, only the right to do so until the expiry date. If the stock price increases by more

than the premium paid, he will profit. If the stock price decreases, he will let the call contract

expire worthless, and only lose the amount of the premium.

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The figure shows the profits/losses for the buyer of a three-month Nifty 1250 call option.

As can be seen, as the spot Nifty rises, the call option is in-the-money. If upon expiration, Nifty

closes above the strike of 1250, the buyer would exercise his option and profit to the extent of

the difference between the Nifty-close and the strike price. The profits possible on this option

are potentially unlimited. However if Nifty falls below the strike of 1250, he lets the option

expire. His losses are limited to the extent of the premium he paid for buying the option.

6.3.2 Long Put :A trader who believes that a stock's price will decrease can buy the right tosell the stock at a fixed price. He will be under no obligation to sell the stock, but has the right

to do so until the expiry date. If the stock price decreases, he will profit by the amount of

the decrease less the premium paid. If the stock price increases, he will just let the put contract

expire worthless.

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The figure shows the profits/losses for the buyer of a three-month Nifty 1250 put option.

As can be seen, as the spot Nifty falls, the put option is in-the-money. If upon expiration, Nifty

closes below the strike of 1250, the buyer would exercise his option and profit to the extent of

the difference between the strike price and Nifty-close. The profits possible on this option can be

as high as the strike price. However if Nifty rises above the strike of 1250, he lets the option

expire. His losses are limited to the extent of the premium he paid for buying the option.

6.3.3 Short Call ( Naked short call): A trader who believes that a stock's price will decrease

can short sell the stock or instead sell a call. Both tactics are generally considered

inappropriate for small investors The trader selling a call has an obligation to sell the stock to

the call buyer at the buyer's option. If the stock price decreases, the short call position will

make a profit in the amount of the premium. If the stock price increases, the short position will

lose by the amount of the increase less the amount of the premium.

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The figure shows the profits/losses for the seller of a three-month Nifty 1250 call option.

As the spot Nifty rises, the call option is in-the-money and the writer starts making

losses. If upon expiration, Nifty closes above the strike of 1250, the buyer would exercise

his option on the writer who would suffer a loss to the extent of the difference between

the Nifty-close and the strike price. The loss that can be incurred by the writer of the option

is potentially unlimited, whereas the maximum profit is limited to the extent of the up-front

option premium of $86.60 charged by him.

6.3.4 Short Put : A trader who believes that a stock's price will increase can sell the right to

purchase the stock at a fixed price. This trade is generally considered inappropriate for a

small investor. If the stock price increases, the short put position will make a profit in the

amount of the premium. If the stock price decreases, the short position will lose by the

amount of the decrease less the amount of the premium.

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The figure shows the profits/losses for the seller of a three-month Nifty 1250 put option.As the spot Nifty falls, the put option is in-the-money and the writer starts making losses.

If upon expiration, Nifty closes below the strike of 1250, the buyer would exercise his

option on the writer who would suffer a loss to the extent of the difference between the

strike price and Nifty-close. The loss that can be incurred by the writer of the option is a

maximum extent of the strike price( Since the worst that can happen is that the asset price

can fall to zero) whereas the maximum profit is limited to the extent of the up-front option

premium of $61.70 charged by him.

6.4 Introduction to Option Strategies

Combining any of the four basic kinds of option trades (possibly with different exercise

prices) and the two basic kinds of stock trades (long and short) allows a variety of

options strategies. Simple strategies usually combine only a few trades, while more

complicated strategies can combine several.

1. Covered Call: Long the stock, short a call. This has essentially the same payoff as a short

put.

2. Straddle: Long a call and long a put with the same exercise prices (a long straddle),

or short a call and short a put with the same exercise prices (a short straddle).

3. Strangle: Long a call and long a put with different exercise prices (a long strangle),

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or short a call and short a put with different exercise prices (a short strangle).

4. Bull Spread: Long a call with a low exercise price and short a call with a higher

exercise price, or long a put with a low exercise price and short a put with a higher exercise price.

5. Bear Spread : Short a call with a low exercise price and long a call with a higher

exercise price, or short a put with a low exercise price and long a put with a higher

exercise price.

6. Butterfly: Butterflies require trading options with 3 different exercise prices. Assume

exercise prices X1 < X2 < X3 and that (X1 + X3)/2 = X2

Long butterfly - long 1 call with exercise price X1, short 2 calls with exercise price X2, and

long 1 call with exercise price X3. Alternatively, long 1 put with exercise price X1, short 2

puts with exercise price X2, and long 1 put with exercise price X3.

Short butterfly - short 1 call with exercise price X1, long 2 calls with exercise price X2,

and short 1 call with exercise price X3. Alternatively, short 1 put with exercise price X1,

long 2 puts with exercise price X2, and short 1 put with exercise price X3.

6.5 Black Scholes Option Model

Black Scholes Model has been widely used but it is a complex option pricing model.It is based

on concept of .risk less hedge.. Investor buys stock & simultaneously sells a call option on that

stock. If stock.s price rises, investor earns profit but holder of option will exercise it; that

exercise will cost investor money. If stock price falls,investor will lose on his investment in stock

but gain from option (which will expireworthless if stock price falls). Black Scholes model helps

to set up so that investorends up with risk less position - no matter what stock does, investor .s

portfolio remains constant. Risk less investment yields risk less rate; if return > risk free rate,

arbitrageurs will buy this risk less position & in process push rate of return down.Black Scholes

Model: Given price of stock, its potential volatility, option.s exercise price, life of option & risk-

free rate, there is but one price for the option if it is to meet the equilibrium condition -- that a

portfolio consisting of stock & call option will earn risk free rate.

The assumptions of the Black-Scholes Option Pricing Model

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1. The stock underlying the call option provides no dividends during the call option.s life.

2. There are no transactions costs for the sale/purchase of either the stock or the option.

3. kRF is known and constant during the option.s life.

4. Security buyers may borrow any fraction of the purchase price at the shortterm risk-free rate.

5. No penalty for short selling and sellers receive immediately full cash proceeds at today.s price.

6. Call option can be exercised only on its expiration date (.European.).

7. Security trading takes place in continuous time, and stock prices move randomly in continuous

time.

The three equations that make up the OPM are:

V = P[N(d1)] - Xe -kRFt[N(d2)].

d1 = ln (P/X) + [kRF + (2/2)]t

t

d2 = d1 - t.

Terms in Black-Scholes equation

V = current value of call option

P = current price of underlying stock

N (dio) = probability that a deviation < di will occur in a standard normal distribution. Thus N

(d1) & N (d2) represent area under a standard normal distribution function.

X = exercise, or strike price of option

e = 2.7183

kRF = risk free rate

t = time until option expires (option period)

ln (P/X) = natural logarithm of P/X

2 = variance of rate of return on the stock

What is the value of the following call option according to the OPM?

Assume: P = $27; X = $25; kRF = 6%; t = 0.5 years: 2 = 0.11

V = $27[N(d1)] - $25e-(0.06)(0.5)[N(d2)].

ln($27/$25) + [(0.06 + 0.11/2)](0.5)

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d1 = (0.3317)(0.7071)

= (.07696 + .0575)/.2345 =0.5736.

d2 = d1 - (0.3317)(0.7071) = d1 - 0.2345

= 0.5736 - 0.2345 = 0.3391.

N(d1) = N(0.5736) = 0.5000 + 0.2168

= 0.7168.

N(d2) = N(0.3391) = 0.5000 + 0.1327

= 0.6327.

V = $27(0.7168) - $25e-0.03(0.6327)

= $19.3536 - $25(0.97045)(0.6327)

= $4.0036.

The impact of the following Para-meters have on a call option 0 12345

Current stock price: Call option value increases as the current stock price increases.

Exercise price ( 67895! :78;5,< As the exercise (strike) price increases, a call options

value decreases.

Option period: As the expiration date is lengthened, a call options value increases (more

chance of becoming in the money.)

Risk-free rate: Call option.s value tends to increase as kRF increases (reduces the PV of the

exercise price).

Stock return variance (volatility.): Option value increases with variance of the underlying

stock (more chance of becoming in the money).

Premium (price pay) depends on:

strike (exercise) price-

market price (market - strike) = intrinsic value (intrinsic value =

economic value of exercising immediately)

time until expiration = time value

short term interest rates

volatility

anticipated cash payments on the underlying (div.)

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Option Pricing

7. Interest Rate Derivatives:

7.1 Introduction

An interest rate derivate is a derivative security where the underlying asset is the

right to pay or receive a (usually notional) amount of money at a given interest rate.

Interest rate derivatives are the largest derivatives market in the world. Market

observers estimate that $60 trillion dollars by notional value of interest rate

derivatives contract had been exchanged by May 2004.

According to the International Swaps and Derivatives Association, 80% of the world's

top 500 companies at April 2003 used interest rate derivatives to control their cash

flow. This compares with 75% for foreign exchange options, 25% for commodity

options and 10% for equity options.

The various interest rate futures contracts traded on exchanges worldwide provide an

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array of portfolio hedging and cross-hedging mechanisms for financial instruments

such as mortgages or high-grade corporate bonds. A long hedge correlates to falling

interest rates, while a short hedge would be used for risk management when rising

interest rates are anticipated. For example, the manager of a bond portfolio who

foresees rising interest rates could hedge by selling T-Bond futures. As interest rates

raise, the price of the T-Bond contract falls, thus, short selling the appropriate number

of T-Bond contracts vis-e-vis the value of the bond portfolio would provide a hedge

against the de-valued portfolio. Similarly, a long-hedge can be used to by a fund

manager to lock in the price he/she will pay to add Treasury Bonds to the portfolio:

7.2 Points of Interest: What Determines Interest Rates?

Interest rates can significantly influence people's behaviour. When rates decline,

homeowners rush to buy new homes and refinance old mortgages; automobile buyers

scramble to buy new cars; the stock market soars, and people tend to feel more

optimistic about the future.

But even though individuals respond to changes in rates, they may not fully

understand what interest rates represent, or how different rates relate to each other.

Why, for example, do interest rates increase or decrease? And in a period of changing

rates, why are certain rates higher, while others are lower?

An interest rate is a price, and like any other price, it relates to a transaction or the

transfer of a good or service between a buyer and a seller. This special type of

transaction is a loan or credit transaction, involving a supplier of surplus funds, i.e., a

lender or saver, and a demander of surplus funds, i.e., a borrower.

7.2.1 Supply and Demand

As with any other price in our market economy, interest rates are determined by the

forces of supply and demand, in this case, the supply of and demand for credit. If the

supply of credit from lenders rises relative to the demand from borrowers, the price

(interest rate) will tend to fall as lenders compete to find use for their funds. If the

demand rises relative to the supply, the interest rate will tend to rise as borrowers

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compete for increasingly scarce funds.

7.2.2 Expected Inflation

Inflation reduces the purchasing power of money. Each percentage point increase in

inflation represents approximately a 1 percent decrease in the quantity of real goods

and services that can be purchased with a given number of dollars in the future. As a

result, lenders, seeking to protect their purchasing power, add the expected rate of

inflation to the interest rate they demand. Borrowers are willing to pay this higher rate

because they expect inflation to enable them to repay the loan with cheaper dolla$

If lenders expect, for example, an eight percent inflation rate for the coming year and

otherwise desire a four percent return on their loan, they would likely charge

borrowers 12 percent, the so-called nominal interest rate (an eight percent inflationpremium plus a four percent "real" rate).

7.2.3 Economic conditions: All businesses, governmental bodies, and households

that borrow funds affect the demand for credit. This demand tends to vary with general

economic conditions. When economic activity is expanding and the outlook

appears favourable, consumers demand substantial amounts of credit to finance

homes, automobiles, and other major items, as well as to increase current

consumption. With this positive outlook, they expect higher incomes and as a result

are generally more willing to take on future obligations. Businesses are also optimistic

and seek funds to finance the additional production, plants, and equipment needed to

supply this increased consumer demand. All of this makes for a relative scarcity of

funds, due to increased demand. On the other hand, when sales are sluggish and the

future looks grim, consumers and businesses tend to reduce their major purchases, and

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lenders, concerned about the repayment ability of prospective borrowers, become

reluctant to lend. As a result, both the supply and demand for credit may fall. Unless

they both fall by the same amount, interest rates are affected.

7.2.4 Federal Reserve Actions: As we have seen, the Fed acts to influence the

availability of money and credit by adjusting the level and/or price of bank reserves.

The Fed affects reserves in three ways: by setting reserve requirements that banks

must hold, as we discussed earlier; by buying and selling government securities

(usually U.S. Treasury bonds) in open market operations; and by setting the "discount

rate," which affects the price of reserves banks borrow from the Fed through the

"discount window."

7.2.5 Fiscal Policy: Federal, state and local governments, through their fiscal policy

actions of taxation and spending, can affect either the supply of or the demand for

credit. If a governmental unit spends less than it takes in from taxes and other sources

of revenue, as many have in recent years, it runs a budget surplus, meaning the

government has savings. As we have seen, savings are the source of the supply of

credit. On the other hand, if a governmental unit spends more than it takes in, it runs a

budget deficit, and must borrow to make up the difference. The borrowing increases

the demand for credit, contributing to higher interest rates in general.

7.3 Interest Rate Predictions

General economic conditions, for example, cause all interest rates to move in the

same direction over time. Other factors vary for different kinds of credit transactions,

causing their interest rates to differ at any one time. Some of the most important of

these factors are:

1. Different levels and kinds of risk

default risk

liquidity risk

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maturity risk

2. Different rights granted to borrowers and lenders

Coupon and zero-coupon bonds

Convertible bonds.

Call provisions

Put provision

3. Different tax considerations

7.4 Forward rate agreement (FRA)

Let us assume that you have agreed to a loan with a floating interest rate. If the

general level of interest rates rose, you would normally be exposed to a higher interest

burden. But the purchase of a forward rate agreement (FRA) offers protection: if

money market rates rise, the FRA pays you the difference between the interest rate

fixed in the FRA and the prevailing market interest rate

You can protect your investment income against falling interest rates by selling the

FRA. If interest rates fell below the agreed threshold, FRA will compensate you for

the reduced return

Let us assume that you have taken out a two-year loan with a bank for EUR 5 million,

with interest payments linked to the six-month EURIBOR. The interest rate fixed for

the six-month period starting today is 4.0% p.a. The future development of the six-

month EURIBOR is uncertain today, which exposes you to risk. For that reason, you buy a FRA,

with a six-month hedging period, starting in six months' time (a so-called

6x12 FRA) at a rate of 5.5%.

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If, for example, over the next six months the six-month EURIBOR were to rise to

6.5%, without this contract you would be subject to 1.0% higher interest for this

interest period. Thanks to the FRA, which compensate you for these additional costs,

leaving your interest expense at 5.5% plus your loan margin. Contrary to your

expectations: in this case, your interest income will fall short of the anticipated level.

You can offset this risk by purchasing a floor. If, on the fixing day for your floor

contract, the prevailing EURIBOR rate is lower than the agreed floor rate, you will be

compensated to the extent of this differential.

When you buy a floor you pay only the option premium, with no subsequent costs

incurred.

8. Interest rate options

8.1 Hedging Pre-Issue Pricing Risk for Fixed-Rate Debt

Many companies today are considering the issuance of fixed-rate debt to lock in cost-

effective funding and strengthen their capital base. Interest rates, however, don't

always cooperate. Fortunately, there are a number of hedging tools available which

can reduce the impact of interest rate fluctuations on prospective debt issues or private

placements during the structuring and marketing period before pricing.

The Challenge

Companies planning to issue fixed-rate debt are exposed to the risk of Treasury rate

movements until the new issue is priced. Even the briefest waiting period can

significantly increase exposure. To address this challenge, issuers can choose from a

variety of off balance sheet risk management techniques to synthetically hedge the

yield on the Treasury security on which the debt will be priced.

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For Example

Consider a company that decides today to borrow $100mm for 10 years, with the

proposed issue to be priced in six weeks. The company does not want to speculate on

the direction of interest rates, and seeks to reduce its exposure until the issue is priced.

Until the debt is priced, the company faces exposure to changes in the underlying

Treasury rate; and un hedged interest rate exposure can translate into real money. For

example, on a $100 million 10-year Treasury with a current yield of 6.56%, the

present value of a one basis point change in rates is $72,000!

As you can see in the table below, the cost impact of even a small change in rates can

be extremely large - higher if rates go up, lower if rates fall. If in markets of even

average volatility, intraday rate movements alone can be as much as 15 basis points

up or down, consider how much is at risk over the typical 1 to 3 month pre-issue

period.

55

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8.2 Hedging Solutions

8.2.1 Caps-Hedging against rising interest rate

You plan to take out a loan, taking advantage of what are presently very attractive

interest rates. Despite the fact that you expect interest rates to rise, you still wish to

participate in the event of falling rates.

The solution for this is a cap. As the buyer of a cap you hedge against the risk of

rising money market rates. If, on the agreed fixing day for your cap, the prevailing

market interest rate, generally EURIBOR, exceeds the maximum interest rate agreed

in the cap contract, cap will pay you the difference between the prevailing market rate

and the agreed cap limit for the current interest period, based on the underlying

notional amount.

The particular advantage of this hedging method is that you continue to benefit

without restrictions from falling money market rates

Example let us assume that you intend to carry out some modernisation measures in

your company. As you do not wish to unnecessarily commit liquid funds, you decide

to take out an investment loan of EUR 1 million. A cap creates a ceiling on floating

rate interest costs. When market rates move above the cap rate, the seller pays the

purchaser the difference. A company borrowing on a floating rate basis when 3 month

LIBOR is 6% might purchase a 7% cap, for example, to protect against a rate rise

above that level. If rates subsequently rise to 9%, the company receives a 2% cap

payment to compensate for the rise in market rates. The cap ensures that the

borrower's interest rate costs will never exceed the cap rate.

8.2.2 Floors-Hedging against falling interest rate

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When investing liquid funds, an attractive return is a key criterion for your decision.

However, if money market rates decline this would, in practice, represent an actual

shortfall in revenue for your company. As a result, you could be missing out on

returns which you may have relied upon in your planning.

You can avoid the resulting uncertainty by buying what is known as a floor. A floor is

an agreement on a minimum interest rate # basically an option on a minimum interest

rate. This protects you against the risk of falling interest rates for a period of up to ten

yea$

If interest rates go up, you will benefit from this rise without restriction.

Investments with a variable rate of interest - such as Floating-Rate Notes - are a

common instrument to benefit from rising money market rates. However, interest

rates might fall -

A floor is the mirror image of a cap. When market rates fall below the floor rate, the

seller pays the difference. A 6% floor triggers a payment to the purchaser whenever

market rates drop below 6%. Asset managers buy floors to guarantee a minimum

return on floating rate assets. They sell floors to generate incrementally higher returns.

Debt managers buy floors to protect against opportunity losses on fixed rate debt

when rates fall. They may sell floors as a component of a hedge strategy involving

other derivative instruments.

8.2.3 Treasury collars (the combination of buying a Treasury cap and selling a

Treasury floor) can be used to hedge current rates within a targeted range. The cap

protects against increases in interest rates. The sale of the floor, which eliminates the

benefit from a decline in rates below the floor rate, reduces the cost of the hedge. A

Treasury collar can be structured at no upfront cost by setting the cap and floor rates

such that the premium received for the floor entirely offsets the premium due for the

cap.

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Combining Caps and Floors to Create Collars

A collar is created by purchasing a cap or floor and selling the other. The premium

due for the cap (floor) is partially offset by the premium received for the floor (cap),

making the collar an effective way to hedge rate risk at low cost. In return the hedger

gives up the potential benefit of favourable rate movements outside the band defined

by the collar. A borrower who purchases an 8% cap