Week 8 : Strategies Introduction Assume that the underlying asset is a stock paying no income Assume that the options are EUROPEAN Ignore time value of money In figures o Dashed line relationship between profit and stock price for the individual security o Solid line relationship between profit and stock price for the entire portfolio 3 Alternative Option Trading strategies o Take position in the option & the underlying o Take position in 2 or more options of the same type (Spread) o Combination : Take a position in a mixture of calls & puts (Combination) (Apply when you already own the option and know the movement) Using Position in an Option & the Underlying Writing a Covered Call Selling a call and simultaneously buying the underlying stock Known as synthetic short put Use when expecting stock price to rise (buy for less, sell for more) Short Call Long Stock Short Put (OUTCOME) Counterparty will let call lapse and my payoff will be premium Loss; I bought stock at higher price than the current market price Loss is slightly less than holding the stock alone by the amount of premium Counterparty will exercise call against me & my payoff My extra gain from my long position stock is offset by loss
=-(St X) + premium Reverse of Writing a Covered Call I make gain; bought stock at lower price than the current market price Buying a call and simultaneously selling the underlying stock Known as synthetic long put Use when expecting stock price to drop from my short call. Payoff is capped at X c Short Stock (Green) Long Put Let my call option lapse and payoff is PREMIUM PAID Gain; I sold stock at higher price than the current market price Gain a little less than holding stock alone; premium for call I exercise my call option. My pay off is =(ST X) Loss; I sold stock at lower price than current market price Protective Put Buying a put Simultaneously buying the underlying stock Known as synthetic LONG CALL Use when expecting stock price to rise My gain in call position is offset by loss in short stock & payoff is capped
Long Put Long Stock Long Call (Outcome) ST <X Exercise my put & payoff : (X ST) premium Loss; I hold stock bought at higher price than current market price Any gain from put is offset by loss on stock position and my payoff is capped Let my put call lapse and pay off is premium Reverse of Protective Put Gain; I bought stock at lower price than the current market price Selling a put and simultaneously selling the underlying stock Known as synthetic short call Use when expecting stock price to drop Gain a little less than holding stock alone by the premium for put Short Put Short Stock Synthetic Short Call Counterparty exercises put against me & my payoff is = - (X- ST) + premium Gain; I sold stock at higher price than market As price drops lower, any extra gain I made on short stock is offset by loss on short put. Payoff is capped at X + premium
Counterparty lets put lapse & my payoff is premium Loss; I sold stock at lower price than current market price Put option lapse and my payoff is loss on stock, compensated by put premium. Loss is slightly less than holding stock alone Spread Bull Spread Using Calls: o Buy a lower strike call and simultaneously sell a higher strike call Using Puts o Buy a lower strike put and simultaneously sell a higher strike put Use when expecting stock price to rise Bull Spread Using Calls Long Call (Grey) Short Call (Green) Outcome (Yellow) 1 Let call lapse and payoff is premium 1 Exercise my call and my payoff : (St X1) Premium 2 My counterparty will let call lapse and my payoff is premium My counterparty will exercise call against me. My Payoff is: -(ST X2) + premium 1 Both calls are lapsed and my payoff : =premium (initial investment for bull spread using call) X1 < 2 I exercise my call and my counterparty will let call lapse. I more than I only holding Long call by: Premium from short call Both calls are exercised & their payoff cancel each other out. My payoff is capped : (X2-X1) Net Premium
Stock Price Range Payoff from Long Calll Payoff from Short Call Total payoff 1 0 0 0 K1 < ST < K2 ST K1 0 ST K1 ST K1 K2 ST K2-K1 Bull spread using Puts Short Put (yellow straight line) Long Put (green dotted line) Outcome (Green Straight line) 2 My counterparty exercises put against me & my payoff = -(X2 ST) + premium 1 I exercise my put and payoff is = (X1 ST) Premium 1 Both puts are exercised & payoff cancel each other out. My payoffs capped at = (X1 ST) + (ST X2) + net Premium X1 < 2 Let my put lapse but counterparty exercise put against me. My payoff is slightly less than if I short put at X2 alone Counterparty let put lapse and my payoff is premium Bear Spread I let my put lapse and my payoff is premium Using Calls o Buy a higher strike call and simultaneously sell a lower strike call Using Puts o Buy a higher strike put and simultaneously sell a lower strike put Use when expecting stock price to drop Both puts are lapsed and my payoff is zero + net premium
Using Calls Long Call Short Call (Green) Outcome 2 Let my call lapsed and my pay off is premium I exercise my call & payoff is: (St X2) premium 1 My counterparty let call lapse & my payoff is premium 1 My counterparty exercise call against me and my payoff is =-(ST X1) + premium 1 Both calls are lapsed & my payoff is zero + net premium (positive); long at lower premium X1 < 2 Let my call lapse but counter party exercise call against me. Payoff is: -(ST X1) + Premium Received premium Both calls are exercised and their payoff cancel each other out. Payoff is capped at = (ST X2) + (X1 ST) = -(X2-X1) + net premium
Using Puts Long Put (Grey dotted line) Short Put (Yellow Line) Outcome (Green Line) 2 I exercise my put and my payoff is: (X2 ST) premium 1 My counterparty exercise put against me & my payoff is = -(X1 ST) + premium 1 Both puts are exercised, their payoffs cancel each other out. My payoff is capped : (X2 St) (X1 ST) = (X2 X1) premium X1 < 2 Exercise my put. Counterparty let put lapse. My payoff : (X2 ST) + premium. Payoff is higher than long put alone by premium Let my put lapse and my payoff is premium Butterfly Spread 1 My counterparty lets put lapse. My payoff is premium No puts are exercised. My Payoff is zero + net premium which is negative; I long put at a higher premium than my short put Using Calls o Buying a call option with a relatively low strike and another call with a relatively high strike o And, selling two call options with the strike price halfway between the low and high strike prices Using Puts o Buying a put option with a relatively low strike and another put with a relatively high strike o And, selling two puts with the strike price halfway between the low and high strike price Use when large stock prices moves are unlikely
Using Calls When you expect narrow movement of stock price Short 2 Calls at Middle (X2) 2 My counterparty lets 2 call lapse & my payoff is premium My counterparty exercise 2 calls against me & my payoff is = -2(ST X2) + premium Long Call at Lower Price (X1) 1 Let my call lapse. Payoff is premium 1 My payoff (ST X1) premium Exercise call Long Call at Higher Strike (X3) 3 Let call option lapse. Payoff is premium 3 Exercise call My payoff (ST X3) premium Outcome 1 None of call options has been exercised. Payoff is zero + net premium (-) X1 < St < X2 I exercise call at X1 and 3 other calls are lapsed. My Payoff (St X1) + net premium (- ) X2 < 3 3 options exercised and 1 lapsed (Call at X3) Counterparty will exercise 2 calls against me. Payoff: (X3 ST) + net Premium (-) 3 All calls are exercised & payoff of all calls cancel each other out. Payoff is net premium Payoff table for Butterfly Spread STOCK PRICE Long Call at X2 Long Call at X3 Short 2 Call at X2 TOTAL
1 (none 0 0 0 0 exercised) X1 < 2 ST X1 0 0 ST X1 X2 < 3 ST X1 0-2(ST X2) (X3 ST) see book for proof) 3 ST X1 ST X3-2(ST X2) 0 Using Put Long Put at Lower Strike (X1) 1 Exercise my put and my payoff is (X1 ST) premium 1 Let my put lapse and my payoff is premium Long Put at Higher Strike (X3) 3 I exercise my put and my payoff = (X3 ST) premium 3 I let my put lapse and my payoff is premium Short 2 Puts at middle (X2) 2 My counterparty exercise 2 puts against me and my payoff : -2(X2 ST) + premium My counterparty let 2 put lapse & my payoff is premium Outcome 1 All puts are exercised and payoffs cancel each other out. Net payoff is premium X1 < 2 Let put at X1 lapse & exercise put at X3. Put at X2 will be exercised against me. Payoff (St X1) X2 < 3 Exercise my put at X3 and remaining 3 puts are lapsed. Payoff = (X3 ST) 3 All puts lapsed and my payoff is zero net premium
Combination Straddle o Buying a put option and a call option at the same strike o Use when large stock price moves are likely (but do not know the direction) Strangle o Buying a put option and a call option at the different strike o Use when large stock price moves are likely (but do not know the direction) Straddle Long a Put Long a Call Outcome I exercise my put & my payoff is (X-ST) premium Let my call lapse and payoff is premium Let call lapse and exercise put, and my payoff is (X-ST), but slightly lower than long the put by premium for call Let put lapse and payoff is premium Exercise my call & my payoff is (ST X) premium Let my put lapse and exercise call and payoff is (ST X) premium for put
Strangle Combination Long Put at Lower Strike (X1) Long Call at Higher Strike (X2) Outcome 1 Exercise my put and payoff is (X1 ST) premium 2 Let my call lapse and my payoff is premium 1 Exercise put and let call lapse. Gain from put will be less, due to the premium for call X1 < 2 Both put and call are lapsed. Payoff will be the premium for both 1 Let my put lapse and my payoff is premium Exercise my call and my payoff is = (ST X2) premium Gain from exercising call option will be less, due to the premium for letting put option lapse