Risk Management using Options

Risk Management using Options OptionsOptions are the most recent and evolved derivative contracts. They have non linear or asymmetrical profit profiles making them fundamentally very different from futures and forward contracts.An option gives the holder of the option the right to do something in future. The holder does not have to exercise this right. An option is a legal contract which gives the holder the right to buy or sell a specific amount of underlying asset at a fixed price within a specified period of time.

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4OPTION TYPESStock Options

Index Options

Foreign currency options

Interest rate options

Futures options

PARTIES TO THE OPTIONS CONTRACTOption Exchange------------------------OTCBUYERLong PositionSELLERShort PositionOption Terminology Index options: Have the index as the underlying. They can be European or American. They are also cash settled.Stock options: They are options on individual stocks and give the holder the right to buy or sell shares at the specified price. They can be European or American.Buyer of an option: The buyer of an option is the one who by paying the option premium buys the right but not the obligation to exercise his option on the seller/writer.Writer of an option: The writer of a call/put option is the one who receives the option premium and is thereby obliged to sell/buy the asset if the buyer exercises on him.Call option: It gives the holder the right but not the obligation to buy an asset by a certain date for a certain price.Put option: It gives the holder the right but not the obligation to sell an asset by a certain date for a certain price.Option price/premium: It is the price which the option buyer pays to the option seller. It is also referred to as the option premium.Expiration date: The date specified in the options contract is known as the expiration date, the exercise date, the strike date or the maturity.Strike price: The price specified in the options contract is known as the strike price or the exercise price.American options: These can be exercised at any time up to the expiration date.European options: These can be exercised only on the expiration date itself. European options are easier to analyze than American options.

9 OPTION POSITIONS

Buy call Buy put

Write call Write put

10PROFITABILITY OF OPTIONSS=Stock price & x= exercise pricePriceCall OptionPut OptionS > XIn the MoneyOut of the MoneyS = X

At the MoneyAt the MoneyS < XOut of the MoneyIn the Money

11Stock Price (S)Strike Price (X)ConditionStatus for callStatus for put270360S < XOTMITM300360S < XOTMITM360360S = XATMATM400360S > XITMOTM450360S > XITMOTM500360S > XITMOTMEXERCISE FOR OTM, ITM & ATMOption Terminology In-the-money option: An in-the-money (ITM) option would lead to a positive cash flow to the holder if it were exercised immediately. A call option on the index is said to be in-the-money when the current index stands at a level higher than the strike price (i.e. spot price > strike price). If the index is much higher than the strike price, the call is said to be deep ITM. In the case of a put, the put is ITM if the index is below the strike price.At-the-money option: An at-the-money (ATM) option would lead to zero cash flow if it were exercised immediately. An option on the index is at-the-money when the current index equals the strike price (i.e. spot price = strike price).Option Terminology Out-of-the-money option: An out-of-the-money (OTM) option would lead to a negative cash flow if it were exercised immediately. A call option on the index is out-of-the money when the current index stands at a level which is less than the strike price (i.e. spot price < strike price). If the index is much lower than the strike price, the call is said to be deep OTM. In the case of a put, the put is OTM if the index is above the strike price.Option Terminology The option premium has two components intrinsic value and time value. Intrinsic value of an option at a given time is the amount the holder of the option will get if he exercises the option at that time. The intrinsic value of a call is Max[0, (St K)] which means that the intrinsic value of a call is the greater of 0 or (St K). Similarly, the intrinsic value of a put is Max[0, K St],i.e. thegreater of 0 or (K St). K is the strike price and St is the spot price.Option Terminology Time value of an option: The time value of an option is the difference between its premium and its intrinsic value. Both calls and puts have time value. The longer the time to expiration, the greater is an options time value, all else equal. At expiration, an option should have no time value.

Intrinsic valueIntrinsic value of call option = Max (0, So - E)Intrinsic value of put option = Max (0, E - So)Time valueTime value of a call option = C [Max(0, So - E)]Time value of a put option = P [Max(0, E - So)]

Futures Vs Options1.Linear pay off2.Both long and short are at risk3.Price of the asset is determined by the market forces4.Buyer and seller need not pay premium5.Both the parties must deposit margin money6.Maximum loss to both buyer and seller is unlimited7.Futures do not have different strike prices 1.Non linear payoff2. Only short is at risk3.Price of the option is determined by market forces4. Buyer must pay the premium to the seller5.Only the seller must pay the margin money6.Maximum loss to the buyer is limited to the premium paid.7.Options are available at different strike prices.

1. Payoff profile of buyer of asset: Long assetIn this basic position, an investor buys the underlying asset, Nifty for instance, for 2220, and sells it at a future date at an unknown price, St. Once it is purchased, the investor is said to be long the asset. If the index goes up there is a profit else losses.

2. Payoff profile for seller of asset: Short assetIn this basic position, an investor shorts the underlying asset, Nifty for instance, for 2220, and buys it back at a future date at an unknown price, St. Once it is sold, the investor is said to be short the asset. If the index falls, there are profits, else losses

3. Payoff profile for buyer of call options: Long call

4. Payoff profile for writer of call options: Short call

5. Payoff profile for buyer of put options: Long put

6. Payoff profile for writer of put options: Short put

Option trading strategies1. Long stock long putConsider an investor who buys a share for Rs.100. To guard against the risk of loss from a fall in price, he buys a put for Rs.16 for an exercise price of Rs.110. Explain how this position will perform in different price scenarios on expiration.Solution:Share price Rs.100Net profit = P/L on option + P/L on share- premium

Share priceExercise priceP/L on optionP/L on sharePremiumNet profit70110110-70 = 4070-100 = -3016-68011030-2016-69011020-1016-610011010016-611011001016-6120110--20164130110--301614140110--401624Option trading strategies2. Short stock long callAn investor shorts a share at Rs. 100 and buys a call option for Rs. 4 with a strike price of Rs.105. How will this position perform?Solution:Share priceExercise priceP/L on optionP/L on sharePremiumNet profit90105--104695105--541100105--04-4105105---54-91101055-104-911510510-154-912010515-204-9Option trading strategies3. long stock Short callAn investor who has bought a share for Rs.100 and who writes a call with a exercise price of Rs.105 and receives a premium of Rs.3. How will this position perform?Solution:Share priceExercise priceP/L on optionP/L on sharePremiumNet profit90105---103-795105---53-2100105--033105105--538110105-51038115105-101538120105-152038Option trading strategies4. Short stock Short putAn investor short a share at Rs. 100 and write a put option for Rs.3 having an exercise price of Rs.100. Prepare a profit/Loss profile for this position.Solution:Share priceExercise priceP/L on optionP/L on sharePremiumNet profit90100-10103395100-55331001000033105100---53-2110100---103-7115100---153-12120100---203-17

32Spreads and combinations-Trading strategiesSpread: A spread position is taken by taking position in two or more options of the same type (call or put options). Imp. Spread strategies are bull spread, bear spread, butterfly spreads, box spread, calendar spread etc.

Combinations: In combination trading strategies one takes position in both calls and puts on the same stock. Imp. Combination strategies are straddles, strips, straps and strangles.

33Combinations- trading strategies Combinations are trading strategies where the trader takes positions in both call and put options on the same stock.

StraddleStripsStrapsStrangle Condor

34Straddle This is an appropriate strategy when an investor is expecting a large move in a stock price but does not know the direction of the move.One can buy the straddle or sell the straddle.Sellers position is reverse of that of the buyer.

35STRADDLE STRATEGY-purchase Buy both call and put on the same stock and same strike price and expiry date (in Rs.)Stock priceStrike priceCall premiumPut premiumP/L701105332801105322901105312100110530211011053-81201105302130110531214011053221501105332

36STRADDLE STRATEGY : PAY OFF(bottom straddle)

37STRIPS STRATEGY Long position in one call and two puts(When we feel greater likelihood of decrease in price) (in Rs.)Stock priceStrike priceCall premiumPut premiumP/L7011053X2=6698011053X2=6499011053X2=62910011053X2=60911011053X2=6-1112011053X2=6-113011053X2=6914011053X2=61915011053X2=629

38STRIPS STRATEGY Long position in one call and two puts

39STRAP STRATEGY Long position in two calls and one put(When we feel greater likelihood of increase in price)(in Rs.)Stock priceStrike priceCall premiumPut premiumP/L701105X2=10327801105X2=10317901105X2=10371001105X2=103-31101105X2=103-131201105X2=10371301105X2=103271401105X2=103471501105X2=10367

40STRAP STRATEGY Long position in two calls and one put

41STRANGLE STRATEGY Long position in put and call option with same expiry date different exercise price Put exercise price(100) < call exercise price(110)

Stock priceStrike priceCall premiumPut premiumP/L70100/110532280100/110531290100/110532100100/11053-8110100/11053-8120100/110532130100/1105312140100/1105322150100/1105332

42STRANGLE STRATEGY(squeeze neck to kill)

43Condor Here the trader takes positions in 4 options at 4 strike prices. It can be long condor or short condor.

Long condor (using calls): Here the trader buys 2 call options at the extreme strike prices(E1 and E4) and sells 2 call options at the middle strike prices(E2 and E3)

44Strike prices and premium (Rs.)E2-E1=E4-E3 and E3-E1=2(E2-E1)Strike prices Strike prices of callsPremiumE190-17 (Buys)E2100+9 (Sells)E3110+5 (Sells)E4Net120-2 (Buys)-5Option GreeksIn mathematical finance, the Greeks are the quantities representing the sensitivity of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent.The name is used because the most common of these sensitivities are often denoted by Greek letters. Collectively these have also been called the risk sensitivities, risk measures or hedge parameters.Option GreeksDELTATHETAGAMMAVEGARHOOption Greeks DELTA The amount by which the price of an option changes as compared to a $1 increase in the price of a stock expressed as a decimal or percentage.

THETA The amount that the price of an option changes as compared to the passage of time [typically 1 day], which is a negative number because the value of the option decreases with time.

GAMMA- The amount that DELTA changes as compared to a $1 increase in the price of the stock which may be important where the DELTA becomes particularly sensitive to changes in the stock price. Option GreeksVEGA is the measure of volatility in the underlying stock, the amount the option price changes with an increase in volatility.

RHO - the amount that the price of an option changes as compared to a unit increase in the risk free rate (i.e., short term US Treasury Bill rate), the least important Greek because most options are short term in nature and so interest costs are a smaller component of the overall change in the option price.