Option Contract (Imran)

8/2/2019 Option Contract (Imran)

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In finance, an option is a derivatives financial instruments that specifies a

contract between two parties for a future transaction on an asset at a

reference price (the strike).The buyer of the option gains the right, but not

the obligation, to engage in that transaction, while the seller incurs the

corresponding obligation to full fil the transaction. The price of an option

derives from the difference between the reference price and the value of

the underlying asset (commonly a stocks, a bond, a currency or a futurecontract) plus a premium based on the time remaining until the expiration

of the option. Other types of options exist, and options can in principle be

created for any type of valuable asset.

Option


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Types of Option

Exchange-traded options

It is(also called "listed options") are a class of exchange traded

derivatives. Exchange traded options have standardized contracts, and

are settled through a Clearing House with fulfillment guaranteed by

the credit of the exchange. Since the contracts are standardized,

accurate pricing models are often available. Exchange-traded options

include:

Stock Option,

Bond Option and Other Interest Rate Option

Stock Market Index Option or, simply, index options and


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Over the Counter Option

It is(OTC options, also called "dealer options") are traded between

two private parties, and are not listed on an exchange. The terms of an

OTC option are unrestricted and may be individually tailored to meet

any business need. In general, at least one of the counterparties to an

OTC option is a well-capitalized institution. Option types commonly

traded over the counter include:

interest rate options

currency cross rate options


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Other option types

Another important class of options, particularly in the U.S.,

are employee stock option, which are awarded by a company to their

employees as a form of incentive compensation. Other types of options

exist in many financial contracts, for example real estate option are often

used to assemble large parcels of land, and prepayment options areusually included in mortgage loans. However, many of the valuation

and risk management principles apply across all financial options.


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European option an option that may only be exercised on expiration.

American option an option that may be exercised on any trading day

on or before expiry.

Bermudan option an option that may be exercised only on specified

dates on or before expiration.

Barrier option any option with the general characteristic that the

underlying security's price must pass a certain level or "barrier" before it

can be exercised.

Exotic option any of a broad category of options that may include

complex financial structures.[7]

Vanilla option any option that is not exotic.

Types of Option Styles
http://en.wikipedia.org/wiki/Option_(finance)http://en.wikipedia.org/wiki/Option_(finance)


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Hedging risk with Derivatives

Review of equity options

Review of financial futures

Using options and futures to hedge portfolio risk

Introduction to Hedge Funds


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Options -- Contract

Calls and Puts

Underlying Security (Number of Units)

Exercise or Strike Price

Expiration date Option Premium

American, European, Asian, etc.


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Options -- Markets

1 Buyer + 1 Seller (writer) = 1 Contract

Examples of Price Quotations

Premium = Intrinsic Value + Time Prem

Options available on Equities

Indicies

Foreign Currencies

Futures


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Options -- Basic Strategies

Buy Call

Sell (write) Call

Buy Put

Sell (write) Put


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Options -- Advanced Strategies

Straddle

Strips and Straps

Vertical Spreads

Bullish Bearish


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Options - Determinants of Value

Value of Underlying Asset

Exercise Price

Time to Expiration

VOLATILITY Interest Rates

Dividends


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Options -- Black Scholes Option

Pricing Model C = SN(d1) - Xe

-rTN(d2)

ln(S/X) +(r+s2/2)Td1 = ---------------------------sT1/2

d2 = d1 - sT1/2

Put-Call Parity: P = C + Xe-rT - S


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Futures Contract

Agreement to make (sell) or take (buy) delivery of aprespecified quantity of an asset at an agreed upon price at aspecific future date.

ex. S&P 500 Index Futures:

Price: 1126.10; Delivery month: June

Buyer agrees to purchase a portfolio representing the S&P500 (or its cash equivalent) for $1126.10 x 250 = $281,525 onThursday prior to 3rd Friday in June. (Buyer is locking in thepurchase price for the portfolio.)

Seller agrees to deliver the portfolio described above.

Note: since this is a cash settled contract, if the price was1116.10 on the delivery date, the buyer would pay the seller$2,500 (= 10 x 250). If the price was 1136.10, the seller wouldpay the buyer $2,500


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Futures Contract: Marking to

Market Marking to market:

Price of Futures contract is reset every day

Gains/Losses versus previous day are posted to buyer and

seller margin accounts Futures = a bundle of consecutive 1-day forward contracts

If futures held to expiration, effective delivery price is sameas when contract initiated


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Futures Contract: Marking to

Market example (C$ contract)11/2 $0.7483 $2000

11/3 $0.7490 +$70 $2070

11/4 $0.7480 -$100 $1970

11/5 $0.7472 -$80 $1890

11/8 $0.7422 -$500 $1390 Add $610

11/9 $0.7430 +$80 $2080

11/10 $0.7432 +$20 $2100


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Speculators often sell index futures when they expect theunderlying index to depreciate, and vice versa.

Index Futures Market

1. Contract to sellS&P @ 1126.1

($281,525) on June17.

April 4

2. Buy S&P @ 1106.1($276,525) on spot

market and deliver @1126.1

June 17

3. Profit = $5,000


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Index futures may be sold by investors to hedge risk associatedwith securities held.


1.Contract to sell S&P @1126.1 ($281,525) on

June 17.

April 4

2. Market falls to1106.1.Gain =$5000

June 17

3. Gain offsets (approx.)loss of $5000 onsecurities held


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Most index futures contracts are closed out before theirsettlement dates (99%).

Brokers who fulfill orders to buy or sell futures contracts earn a

transaction or brokerage fee in the form of the bid/ask spread.



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Hedging with Derivatives

Basic option strategies

Covered call

Protective put

Synthetic short Basic futures strategies

Using interest rate futures to reduce risk


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Covered Call

Sell call on stock you own. (Long stock, short call)

Good: As value of stock falls, loss is partially offset by premium

received on calls sold.

Essentially costless since hedge generates a cash inflow

Bad: Maximum inflow from call = premium; Hedge is less

effective for large drop in stock price

If stock price rises, call will be exercised; Investor transfersgains on stock to holder of call.


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Protective Put

Buy put on stock you own. (Long stock, long put)

Good:

As value of stock falls, loss is partially offset by gain in valueof put. Gain from put continues to grow as stock price falls. If stock price rises, maximum loss on put = premium;

Investor keeps all stock gains less fixed put premium.

Bad: More expensive to hedge with put


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Synthetic Short

Sell call and buy put on stock you own. (Long stock, short call,long put)

Good: As value of stock falls, loss is offset by gain in value of put. Gain

from put continues to grow as stock price falls. If stock price rises, gain is offset by loss on call. Loss from call

continues to grow as stock price rises. Very effective hedging device Can be self-financing (premium received on put sold offsets

premium paid on call purchased)

Bad: Often more expensive than simply shorting the stock itself.


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Delta Hedging with Options

Call Delta = DC= dC/dS

From Black-Scholes model,DC = N(d1)

Ex.: If S=74.49, X=75, r=1.67%, s =38.4%,t=0.1589 yrs.

Then, C = 4.40 and N(d1) = 0.5197

If S increases by $1, C increases by $0.5197

Hedge Ratio = H = 1/DC = 1/0.5197 = 1.924

Sell 1.924 calls per share of stock held to hedge!


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Example of Call Hedge Held toExpiration, 1000 share stock position

IBM Profit S Profit C Combined90 15,510 -20,140 -4,63085 10,510 -10,640 -13080 5,510 -1,140 4,37075 510 8,360 8,870

74.49 0 8,360 8,36070 -4,490 8,360 3,87065 -9,490 8,360 -1,13060 -14,490 8,360 -6,13055 -19,490 8,360 -11,130


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Delta Hedging - Puts

Put Delta = DP= dP/dS From Black-Scholes model and Put-Call Parity,

DP= DC 1 =N(d1) - 1

Ex.: If S=74.49, X=75, r=1.67%, s =38.4%,t=0.1589 yrs.Then, C = 4.40, P = 4.71, N(d1) = 0.5197,and N(d1) -1 = -0.4803

If S increases by $1, P decreases by $0.4803Hedge Ratio = H = 1/D = 1/0.4803 = 2.082Buy 2.082 puts per share of stock held to hedge!


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Example of Put Hedge Held toExpiration, 1000 share stock position

IBM Profit S Profit P Combined90 15,510 -9,891 5,61985 10,510 -9,891 61980 5,510 -9,891 -4,38175 510 -9,891 -9,381

74.49 0 -8,820 -8,82070 -4,490 609 -3,88165 -9,490 11,109 1,61960 -14,490 21,609 7,11955 -19,490 32,109 12,619


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Delta Hedging with Options

Delta changes over time!

S changes

Time declines

Other factors (r, s) may change


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True Delta Hedging Adjust hedge when S changes

Scenarios 1 & 2:

IBM stock drops by $1 to $73.49 ==> Loss of $1000 Call options also drop by $0.5197 ==> Gain of $1037.97

==>Net change $37.97

IBM stock rises by $1 to $75.49 ==> Gain of $1000

Call options also rise by $0.5193 ==> Loss of $1037.97

==> Net change ($37.97)


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True Delta Hedging Adjust hedge when t changes

Scenario 3: One week passes, IBM stock at $71.49 ==> Loss of $3000 Call options now worth $2.73 ==> Gain of $3173

==>Net change $173

New call delta = 0.4029 New hedge ratio = 1/0.4029 = 2.482 ==> Sell 5 more contracts!

Scenario 4: One week passes, IBM stock at $77.49 ==> Gain of $3000

Call options now worth $5.82 ==> Loss of $2698==> Net change ($302) New call delta = 0.6238 New hedge ratio = 1/0.6238 = 1.603 ==> Buy 3 contracts!


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True Delta Hedging Adjust hedge when S changes

Scenarios 1 & 2:

IBM stock drops by $1 to $73.49 ==> Loss of $1000 Put options also rise by $0.4803 ==> Gain of $1008.63

==>Net change $8.63

IBM stock rises by $1 to $75.49 ==> Gain of $1000

Put options also fall by $0.4803 ==> Loss of $1008.63

==> Net change ($8.63)


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True Delta Hedging Adjust hedge when t changes

Scenario 3: One week passes, IBM stock at $71.49 ==> Loss of $3000 Put options now worth $6.06 ==> Gain of $2835

==>Net change ($165)

New put delta = 0.4028 1 = -0.5972 New hedge ratio = 1/0.5972 = 1.674 ==> Sell 4 contracts!

Scenario 4: One week passes, IBM stock at $77.49 ==> Gain of $3000

Put options now worth $3.15 ==> Loss of $3276==> Net change ($276) New put delta = 0.6238 1 = -0.3762 New hedge ratio = 1/0.3762 = 2.658 ==> Buy 5 more contracts!


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Delta Hedging with options

Delta represents response of call (or put) price withchange in the stock price

Delta changes as stock price, time to expiration,interest rates, volatility change

It is too expensive to hedge individual stock positionswith matching options. It is more common to hedge

a portfolio with index options (cross hedging)

Most managers monitor delta itself to decide when torebalance.


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A True Protective Put

Puts can be used to build a floor under the value of a longposition

Buy 1 put per long share

Ex.: Long 1000 shares of IBM at $74.49 Buy 1000 puts at $4.71

Puts guarantee a value of $75 per share

This is insurance, not a hedge!


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A True Protective Put

IBM Profit S Profit P Combined90 15,510 -4,710 10,80085 10,510 -4,710 5,80080 5,510 -4,710 80075 510 -4,710 -4,200

74.49 0 -4,200 -4,20070 -4,490 290 -4,20065 -9,490 5,290 -4,20060 -14,490 10,290 -4,20055 -19,490 15,290 -4,200


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Hedging with Futures (example from May 2001)

There are futures on the S&P500. Suppose I have a portfoliothat is currently worth $1,117,672. The portfolio has a beta of1.3.

June S&P500 futures are at 1430.70

==> contract is worth 500 x 1430.70 = $715,350 Hedge ratio =

(Value of portfolio / Value of Futures contract)(Portfolio Beta)

= (1,117,672/715,350)(1.3) = 2.031 ==> Sell 2 Contracts !


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Hedging with Futures (example from May 2001)

S&P Spot

in June

%

ch

an

ge Port. inJune%

cha

ngeProfit

Portf

olioProfit

Futur

es Combined1573.75 10% 1,262,969 13.0% 145,297 -143,050 $2,2471502.25 5% 1,190,321 6.5% 72,649 -71,550 1,099

1430.7 0% 1,117,672 0.0% 0 0 01359.15 -5% 1,045,023 -6.5% -72,649 71,550 -1,099

1287.65 -10% 972,375 -13.0%-

145,

297 143,050 -2,247


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Adjusting Systematic Risk with Futures

PM may choose to adjust systematic exposure up or down toreflect investor desires expectations of market movements

About index futures: Represents contract to make/take delivery of a portfolio

represented by the index Since index itself may be non-investable, most index futures

contracts are cash-settled example:

S&P500 futures CME contract value = 250 x index Initial margin: $6K for spec, $2.5K for hedgers.


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I have an $11 million stock portfolio with b=1.05. I want toincrease b to 1.2.

Value of Futures = 1314.50 x 250 = $328,625

bf = 1.0. Target b = contribution from portfolio + contribution from

futures 1.2 = (1.0)(1.05) + [(F x 328,625)/$11,000,000](1.0) F = (bT - Wsbs)(Vs/VF)

F = 5.02 => buy 5 contracts What have we done? Used futures contracts to leverage holdings and increase

exposure to market risk


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Suppose target b = .90

0.90 = (1.0)(1.05) + [(F x 328,625)/$11,000,000](1.0)

F = (.90 - 1.05)(33.4728)(1.0) = -5.02 contracts (sell)

We have shorted futures to reduce systematic exposure.


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Hedging with Interest Rate Futures

How do you reduce duration for a bond portfolio? Sell high D, buy low D Sell bonds, buy Tbills Sell interest rate futures

Interest rate futures: agreement to make/take delivery of afixed income asset on a particular date for an agreed upon price

ex: Sept Tbond futures contract $100K FV US Treas bonds with 15-years to maturity and 8%

coupon (what if they don't exist?)

Price: 99-27 = 99 27/32 % of $100,000 = $998,437.50 (Tick = $31.25) D = 8.64 years


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Hedging with Interest Rate Futures

I own an $11,000,000 face value portfolio of high grade UScorporate bonds with an aggregate value of 101-08 (or$11,137,500) and a duration of 7.7 years.

I expect rates to rise. How can I immunize my portfolio? Target D = contribution of bond port + contribution of fut.

0 = (1.0)(7.7) + [(F x 998,437.50)/11,137,500](8.64) F = (0.0 - (1.0)(7.7))(11,137,500/998,437.50)/8.64

F = -9.94 contracts => short 10 Tbond futures contracts

This is the weighted average duration approach


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Option Contract (Imran)

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