Derivatives

Tool for Strategic Investment

Derivatives Defined

• Derivative is a product whose value is derived from the value of underlying asset in a contractual manner.

• In simple terms they are contracts for future delivery of assets and payment for them.

Emergence of the Market

• Can be traced back to the willingness of risk-averse economic agents to guard themselves against uncertainties arising out of fluctuations in asset prices.

• Through the use of derivative products, it is possible to partially or fully transfer price risks by locking in asset prices.

Role of Derivatives

• 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 investors.

Initial Derivative Instruments

• Commodity derivatives• Financial derivatives• 1972 - CME started trading currency futures. • 1973- CBOE – Equity options• 1976 – CME Treasury Bill futures• Now financial derivatives are very popular.• Account for about two-thirds of total transactions

in derivative products.

Factors Driving Growth of Derivatives Use

• Increased volatility in prices in financial markets.

• Increased integration of stock markets world-wide

• Improvement in communication facilities• Development of sophisticated risk

management tools and strategies.• Innovations in derivative markets.

Derivative Markets- Economic Functions

• Derivatives help in discovery of future as well as current prices.

• Helps to transfer risks from those who have them but may not like them.

• Linkage to the underlying cash markets. Cash markets witnesses higher trading volumes because of participation by more players who would not otherwise participate for lack of an arrangement to transfer risk.

Derivative Markets- Economic Functions (contd.)

• Speculative trades shift to a more controlled environment.

• Derivatives have a history of attracting bright, creative, well-educated people with an entrepreneurial attitude. They create new products.

• Help increase savings and investments in the long run. Transfer of risk enables market participants to expand their volume of activity.

Development of Derivative Exchanges

• Chicago Board of Trade (CBOT) in 1848. Exchange for forward contracts.

• In 1865, first futures contract was introduced in CBOT.

• In 1876 “Grain Call” trading established in Kansas City Board of Trade.

Indian Derivatives Market

The Road Ahead

• CASH MARKET• Investments• Day Trading• Rolling Settlement

• Derivatives Market• Hedging• Speculation• Arbitrage

• Index Based• Scrip Based

Stock Index Futures

• Is a derivative contract whose underlying is a stock index.

Why index future??

The market is conditioned to think in terms of the index and therefore would prefer to trade in stock index futures. Further, the chances of manipulation are much lesser

The transaction cost is lower.

Futures Terminology

• Spot price: The price at which an asset trades in the spot market.

• Futures price: The price at which the futures contract trades in the futures market.

• Contract cycle: The period over which a contract trades. The index futures contracts on the NSE have one-month, two-months and three-months expiry cycles.

Futures Terminology (contd.)

• The index futures of a month expire on the last Thursday of the month.

• On the Friday following the last Thursday of the month, a new contract having three-month expiry period would be introduced for trading.

• Expiry Date: It is the last day on which the contract will be traded and at the end of which it will cease to exist.

Futures Terminology (contd.)

• Contract Size: The amount of asset that has to be delivered under one contract. For instance, the contract size on NSE future market is 200 Nifties.

• Future prices normally exceed spot prices.

QUESTION

If you have a portfolio of 2 crores and you expect the market to come

down by 1000 points in the short term, what will be the most

prudent way to reduce your risk?

CHOICES

• Sell your portfolio in the cash market• Ask your Family Astrologer• Use Index Derivatives to hedge your

Portfolio• Do nothing and observe your portfolio

eroding.

Indexes

• In recent years, indexes have come to the forefront owing to direct application in finance in the form of index funds and index derivatives.

• Index derivatvies allow people to cheaply alter their risk exposure to an index(hedging) and to implement forecasts about index movements (speculation)

Purpose of Index Futures

• Hedging• Speculation• Arbitrage

Derivative Market Dynamics• Hedgers – FII’s, Mutual Funds, Pension

Funds, Insurance Companies, HNI’s

• Speculators – Big Operators, HNI’s, Proprietary Traders

Hedging• A Hedge is a combination of positions, where one

position profits and the other position loses.• So a hedge can be thought of as an insurance

against being wrong.• A hedge can help lock existing profit.• Its purpose is to reduce the volatility of a

portfolio, by reducing risk.• Derivatives are widely used for hedging.

Speculation

• Bullish index, long Nifty futures• Bearish index, short Nifty futures

SpeculationBuy(in July) {Spot Nifty-1120}August contract at 1125 NSE Nifty Exposure 1125 x200 = Rs.2,25,000Margin @ 15% = Rs. 33,750/-Sell (after a few days)August Contract at 1165 NSE Nifty at 1160Profit on square off = [1165-1125]x200 = Rs.8000Return on margin = Rs.8000/33750 = 23.70%Amount released on square off =Rs.33750 + Rs.8000

Pay-off for a future buyer

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1065 1085 1105 1125 1145 1165 1185Nifty

Pay-off for a future seller

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1065 1085 1105 1125 1145 1165 1185Profit

Arbitrage• The cash markets and the futures markets are

tightly linked. • On the day of maturity, cash and future market

index converge.• Arbitrageurs bring price uniformity and help price

discovery.• The cash market and index futures provide

arbitrage opportunities which arise due to imbalance between hedgers and speculators.

Arbitrage

• Have funds, lend them to the market• Have securities, lend them to the market

Example

• You own a 1 million portfolio with a beta of 1.25. Current Nifty level 1250. Three month puts at a strike of 1100 are available. How many put contracts should you buy for insuring your portfolio against an index fall below 1100?

• 1. Four• 2. Five• 3. Eight• 4. Ten• The answer is -----

….the answer is

At a spot Nifty level of 1250 for a portfolio value of 1 million with beta of 1.25, the number of puts to buy is (10,00,000*1.25) / 1250 =1000 puts. At a market lot of 200 per contracts you have to buy 5 contracts to insure your portfolio.

Advantage of Futures Trading• Day traders delight

– At a single price buying/selling market lot.– Ability to exit with small movement in price.– Advantage of no circuits– Fear of market lot negated with small price movements

• Highly leveraged position.(double edged sword)• Positions carried overnight based on closing market

trend.• Position can be carried forward for 1-3 months.

Standard Portfolio Analysis of Risk

(SPAN)• A methodology to evaluate risk• Risk-based, portfolio-approach

margining• Part of the VAR family• A flexible framework• Efficient and understandable• An industry-standard

SPAN History

• Developed by CME in 1988• Rapidly adopted by all US futures markets• The standard in financial capitals

worldwide -- Tokyo, Osaka, Singapore, Hong Kong, Sydney, London, Paris, Toronto, New York, Chicago, and now Mumbai

• Numerous other markets are in the “SPAN adoption pipeline”

Uses for SPAN

• Margin (performance bond) calculation

• General-purpose risk analysis• Stress testing• Real-time pre- or post-execution

risk-based credit controls• Risk-based capital requirements

SPAN and margining

• SPAN makes it easy to support cross-margin agreements between clearing organizations

• Scan risk -- the core of SPAN -- determines the worst possible loss assuming perfect correlation of price movements across contract months

SPAN Mechanics• The exchange sets the inputs to SPAN,

modifying them as often as desired• Every day, the exchange calculates SPAN

risk arrays for all of its products and packages all of its SPAN data into its daily SPAN risk parameter file, which is then published

• Members, firms, customers etc. then use the data from the SPAN file, together with their positions data, to calculate SPAN margin requirements

PC SPAN

PC SPAN

Master fileRisk parameter files

Position file

Output /Margin(Report form orfile form- XML)

Options

Options

An instrument which gives the buyer substantial upside potential

but with limited downside risk / cost

Options

• Deferred delivery contracts• give the buyer the right• not the obligation• to buy or sell• a specified underlying• at a set price• on or before a specified date

Option Premium

• Premium : The fee that the buyer pays the option writer up front while buying. It is the maximum loss the buyer can suffer.

• The premium is also referred to as value of the option or price of the option.

Index Options

Index options are European options, which means contracts will be settled on date of expiry only.The date of expiry shall be the last Thursday of the contract month.The contracts shall be available for 1,2 and 3 months.The underlying for Index Options

-for BSE- 30Sensex-for NSE- Nifty

Strike Price or Exercise Price• The price at which the buyer of a call option

has the right (but not the obligation) to purchase the underlying.

• The price at which the buyer of a put option has the right (but not the obligation) to sell the underlying.

Call Option

• Right to BUY a specified underlying at a set price on or before an expiration date.

• The holder of a RIL Dec 500 call option has the right to buy (or go long) 100 RIL shares at a price of 500 anytime between purchase and expiration.

Call Buyer Vs Seller• Call Buyer

– Pays premium– Has choice to exercise to buy the asset

• Call Seller– Collects premium– Has obligation to give the asset

ExampleDeepak is bullish about the index spot nifty 1250.

He decides to buy 3-month Nifty call contract with strike of 1290. Three month later the index closes at 1300. His pay-off on the position is ..

1. Rs.7,0002. Rs.2,0003. Rs.19,0004. None of the above.

Put Option

• Right to SELL a specified underlying at a set price on or before an expiration date.

• The holder of a RIL Dec 250 put option has the right to sell (or go short) a RIL share at a price of 250 anytime between purchase and expiration.

Put Buyer Vs Seller

• Put Buyer– Pays premium– Has choice to deliver asset

• Put Seller– Collects premium– Has obligation to take the asset.

Bearish Index- Buy Puts or Sell Call

Buy Put First time you shall buy when you are bearish in

market.If the index falls you gain and you lose premium if

index moves up.The premium and your belief the fall in index again plays a big role in selection of which PUT to BUY.

Example

• Anand is bearish when Nifty is at 1240.He decides to buy one 2-month put option at strike of 1225 for a premium of Rs.34.50. Two months later Nifty is 1280. His pay-off is :

• Rs. -6900• Rs.-4000• Rs.-5300• Rs.-12000

Types of Options

• American Option– can be exercised any time on or before the

expiration date• European Option

– can be exercised only on the expiration date

Scrip OptionsScrip options shall be American which means it can be settled same dayThe writer of option will be strictly monitored with MTM margins.The value of premium shall be critical and bring in speculators and arbitrageurs to take position.

Option Calculator

The premium calculator helps the user to understand how a change in any one of the factors or more, will affect the option priceProfessional traders for trading & managing the risk of large positions in options & stocks use option Greeks which are available in the option calculator

Option Pricing Models

• Black-Scholes Model– Pce = S*N(d1) - X e -Rf.t * N(d2)– Normal Distribution Function

• Binomial (Cox-Ross-Rubenstein) Model– Ppe = X e -Rf.t * N(-d2) - S*N(-d1) – Binomial Distribution Function

Factors affecting Option Values

Current Price of the underlying asset (S)Exercise Price of the option(X)Time to Expiry (T)Volatility of prices of the underlying asset ()Interest Rates (Rf)

Option GreeksOption Greeks are: 

Delta: is the option Greek that measures the estimated change in option premium/price for a change in the price of the underlying.  Gamma : measures the estimated change in the Delta of an option for a change in the price of the underlying  Vega : measures the estimated change in the option price for a change in the volatility of the underlying. Theta: measures the estimated change in the option price for a change in the time to option expiry.Rho: measures the estimated change in the option price for a change in the risk free interest rates.

Delta (

• Derivative of the option pricing formula with reference to the asset price (S)

• Measures the estimated change in the option premium for a change in S

• For example: If underlying increases by 1 point, a call option whose delta is 0.5 would increase only 0.5 points.

• Delta for futures is always near 100%

Delta

• In-the-money option: Higher Deltas (.8)

• At-the-money option: Average Deltas (.5)

• Out-of-the-money option: Lower Deltas (.2)

Delta

• Deep In-the-money options– Delta converges to 1.00– Premium will typically move bit-by-bit with

underlying• Deep Out-of-the-money options

– Delta converges to Zero– Premium will generally be very unresponsive to

movement in underlying

Knowing an Option’s Delta

• Can Help the Trader– Estimate the change in the option premium

compared to the change in the underlying– Determine the number of options needed to

equal one futures contract.– Determine the probability that the option will

expire in-the-money– In margining and risk analysis

Delta

• Bullish Positions• Long futures• Long call• Short put

Have positive (+) deltas• Bearish Positions

• Short futures• Short call• Long put

Have negative (-) deltas

Understanding “Delta”15 Days to expiry – assumed

Call Strike price

Delta Premiums at different market priceRs.240 Rs.250 Rs.260

200 0.99 40.95 50.85 60.83220 0.88 22.20 31.35 41.05240 0.54 8.30 14.65 22.60260 0.19 2.00 4.60 9.00280 0.04 0.25 0.91 2.40

Gamma (

• Second derivative of the option pricing formula with reference to the asset price (S)

• Measures the estimated change in the delta of the option for a change in S

Sensex 4000 callwith 30 days to expiry

0

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Gam

ma

Gamma

• Sensex call 4000 at Sensex level of 4000• Delta = 0.568 and gamma = 0.002 If Sensex

increases by one point to 4001 then delta (not the premium) will increase by 0.002 points to 0.57 (0.0568 + 0.002). In other words, the option premium will increase or decrease in value by 0.568 point when Sensex rises to 4001 and by 0.057 points when Sensex rises from 4001 to 4002 level.

Gamma• Positive Gamma Position

– Long Calls– Long Puts

• Negative Gamma Position– Short Calls– Short Puts

• (Delta)+(Gamma)=(New Delta) for incremental increase in the underlying

• (Delta)-(Gamma)=(New Delta) for incremental decrease in the underlying

Vega (

• Derivative of the option pricing formula with reference to the volatility of the asset returns ()

• Measures the estimated change in the option premium for a change in

Vega (

• For Sensex Call 4000 at Sensex level of 4000 having 30 days to expire when implied volatility is 20%, interest rate is 10% and dividend yield is nil, the premium is 108 and Vega is 4.50, the premium would increase to 112.50 when implied volatility moves up to 21%.

Vega

• Positive Vega Position– Long Calls– Long Puts

• Negative Vega Position– Short Calls– Short Puts

Vega

• Original Option Premium + Vega = New Option Premium for 1% increase in Implied Volatility

• Original Option Premium - Vega = New Option Premium for 1% de crease in Implied Volatility

Theta

• Derivative of the option pricing formula with reference to the time to option expiry (T)

• Measures the estimated change in the option premium for a change in T

Theta

• For Sensex Call 4000 at Sensex level of 4000 having 30 days to expire when implied volatility is 20%, interest rate is 10% and dividend yield is nil, the premium is 108 and Theta is 2.1, the premium would decrease to 105.9 on next day when days to expiry remains 29.

Rho (

• Derivative of the option pricing formula with reference to the risk free rate (Rf)

• Measures the estimated change in the option premium for a change in Rf

Premium Value• Option premium is based on factors

Intrinsic value Time value Volatility

Intrinsic value

• The difference between strike and spot when it is in-the-money option.

• Intrinsic value is Zero for all out-of-the money option.

Time Value of option

• Value of an option is usually greater than intrinsic value because of probability that spot will rise / fall in future.

• The time value of an option decreases as thetime to maturity decreases.

Intrinsic value & Time ValueCurrent market price of Satyam Rs.240

Call Strike Price

Premium Intrinsic Value

Time Value

200 40.95 40 0.95

220 22.20 20 2.20

240 8.30 0 8.30

260 2.00 0 2.00

280 0.25 0 0.25

Understanding Time value

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No. of balls remaining

Run

rat

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Run RateProbability to win

Volatility

Scrip Volatility STRIKE SPOT Premium

HLL 3% 200 190 5

Satyam 12% 200 190 10

Futures V/s Options

• Trading Futures may be viewed as a one-dimensional game. Only the market price has an impact on your profit and loss.

Futures V/s Options

• Risk- Futures have unlimited & Options buying have limited risk

• Trading Options may be viewed as a two dimensional game. Changes in an:– Option’s underlying price, and/or– Option’s implied volatility will have an impact

on your profit or loss

Index Options -MarginsMargins is the sum of following 3 parts

Part A -SPAN Margin1. Risk Parameter file shall be generated 3 times and

uploaded to trading member for margins.OpeningAfternoon(1.00PM)Closing

2 Net Option Value(NOV)=(Long Option value-Short Option Value)* the number of contracts

Index Options -Margins• Margin (Part A) Span margin-Net Option valuePart B.SEBI prescribed 3% margin on exposure

Future exposure= No.of contracts*50*last closing price*0.03+

Long Option= No exposure margin reqd.+

Short Option= No.of contracts*50*last closing price*0.03

Options trading

Basic Methods:Bullish on index = Buy callBearish on index= Buy PutAnticipate volatility = Buy a Call and a Put at same strike priceSideways Market = Sell a Call and a Put of different strike price

Long Options Contracts

• Highly leveraged positions with limited risk.

– Risk is limited to the original premium paid.

Bullish market- BUY CALLBuying CallThe spot Nifty is 1100. Which call to buy???The call with strike 1060 is deep-in-the-money and hence

has higher premium.The call with strike 1120 is out-of- money and trades at lower premium. The 1180 call is deep-out-of-money and buying this is buying lottery.

Decide your trade based on where you feel the Nifty will move and then the premium comes in play. (Generally at the money call has good chance of making profit)

Pay-off for Call buyer at 1080

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Pay-off

Economic Payoff for Call Option

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Asset Price

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Buy CallSell Call

Bearish on market- Buy Put

Buying Put • First time you shall buy when you are

bearish in market.• If the index falls you gain and you lose only

premium if index moves up.• The premium and your market study on

extent of index fall again plays a big role in selection of which PUT to BUY.

Pay-off for Put buyer at 1120

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Pay-off

Economic Payoff for Put Option

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Buy PutSell Put

Volatile market• BUY a CALL and a PUT at same strikeA variation combining the buy call and buy put

strategy is called a straddle.It involves holding both a long call and long put

position with same strike price and time to expiration.

E.g. Buy Call = 1100 Premium = 10 Buy Put = 1100 Premium = 10

Pay-off for straddle at strike of 1100

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1040 1060 1080 1100 1120 1140 1160

Pay-off

Option Strangles

• Consist of buying a put and buying a call (Long Strangle) with the put strike lower than the call strike, and both option legs have the same expiration;

OR• Consist of selling a put and selling a call

(Short Strangle) with the put strike lower than the call strike, and both options legs have the same expiration

Long Strangles• Maximum loss is equal to net debit, or total

premium paid• Maximum profit is unlimited• Breakeven levels are equal to:

– put strike minus net debit– call strike plus net debit

• Net delta is approximately zero when strikes are equi-distant from current underlying price

Economic Pay off for Long Strangle

-200-100

0100200300400500600

Sensex level

Prof

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Short Strangles

• Maximum profit is equal to net credit• Maximum loss = unlimited• Breakeven levels are equal to:

– put strike minus net credit– call strike plus net credit

• Net delta is approximately zero when strikes are equi-distant from current underlying price

Economic Pay off for Short Strangle

-600

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200

Sensex level

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Bullish on index-Buy Call or Sell puts

Buying CallThe spot nifty is 1250. Which call to buy???The call with strike 1200 is deep-in-the-money and hence

higher premium.The call with strike 1275 is out-of- money and trades at lower premium. The 1300 call is deep-out-of-money and buying this is buying lottery.

Decide your call based on where you feel the Nifty move and then the premium comes in play. (Generally at the money call has good chance of making profit)

Vertical Spreads

• Buying a call (put) and selling a call (put) with different strike prices but the same expiration month.

• Two types of vertical spreads– Bull Spreads– Bear Spreads

Debit / Credit Spreads

• Debit Spreads entail a net pay-out of option premium

• Credit Spreads entail a net collect of option premium

Bear Vertical Spreads

• Bear Call Spread (Credit Spread)• Bear Put Spread (Debit Spread)

Bear Spreads have a negative delta and consist of:– Buying the higher strike call (put)– Selling the lower strike call (put)

Economic Payoff of Bear Spread

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Bear Vertical Spreads

• Maximum loss occurs above upper strike price

• Maximum profit occurs below lower strike price

• Breakeven level equals:– Lower strike plus credit (call spread)– Upper strike minus debit (put spread)

• Have net negative delta, that is, benefit from a decline in market price levels.

Bull Vertical Spreads

• Bull Call Spread (Debit Spread)• Bull Put Spread (Credit Spread)

Bull Spreads have a positive delta and consist of:– Buying the lower strike price call (put)– Selling the higher strike price call (put)

Bull Vertical Spreads

• Maximum loss occurs below lower strike price

• Maximum profit occurs above upper strike price

• Breakeven level equals:– Lower strike plus debit (call spread)– Upper strike minus credit (put spread)

• Have net positive delta, that is, benefit from an increase in market price levels.

Economic Pay off for Bull Spread

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-50

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