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ECO 4378 Instructor: Saltuk Ozerturk Basic Trading Strategies Involving Options

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ECO 4378 Instructor: Saltuk Ozerturk Basic Trading Strategies Involving Options ECO 4378 Instructor: Saltuk Ozerturk Basic Trading Strategies Involving Options Bull Spread: involves a simultaneous purchase of a call option with • strike price X1 and sale of a call option with strike price X2 where X1 <X2. In other words, it involves a long position in a call option with strike price X1 andashortpositioninanothercalloptionwitha higher strike price X2. Example (Bull Spread): Consider a portfolio with — a long position in a call option on a stock with a strike price of • X1 =$30and with a price of $5; and — a short position in a call option on the same stock with a strike price of X2 =$38and with a price of $3. Now let us find the payoff function for this portfolio as a function of ST , the stock price at expiration. If ST < $30, payoff is 5+3= 2 − − If 30 <ST < $38 payoff is ST 30 5+3=ST 32 − − − If ST > $38 payoff is (ST 30) (ST 38) 5+3=6 − − − − Below is the payoff diagram for this bull spread. Payoff Bull 6 Spread 30 38 ST -2 1 Bear Spread: involves a simultaneous purchase of a call option with • strike price X2 and sale of a call option with strike price X1 where X1 <X2. In other words, it involves a long position in a call option with strike price X2 andashortpositioninanothercalloptionwitha lower strike price X1. Example (Bear Spread): Consider a portfolio with — a long position in a call option on a stock with a strike price of • X2 =$40and with a price of $4;and — a short position in a call option on the same stock with a strike price of X1 =$30and with a price of $6. Now let us find the payoff function for this portfolio as a function of ST , the stock price at expiration. If ST < $30, payoff is 4+6=2 − If 30 <ST < $40 payoff is (ST 30) 4+6=32 ST − − − − If ST > $40 payoff is (ST 30) + (ST 40) 4+6= 8 − − − − − Below is the payoff diagram for this bear spread. Payoff Bear Spread 2 30 40 ST -8 2 Straddle: involves a simultaneous purchase of a call option with strike • price X and purchase of a put option with strike price also X. In other words, it involves long positions in a call option and put option both with strike price X. Example (Straddle): Consider a portfolio with — a long position in a call option on a stock with a strike price of • X =$70andwithapriceof$4;and — a long position in a put option on the same stock with a strike price of X =$70and with a price of $3. Now let us find the payoff function for this portfolio as a function of ST , the stock price at expiration. If ST < $70, payoff is (70 ST ) 4 3=63 ST − − − − If ST > $70 payoff is (ST 70) 4 3=ST 77 − − − − Below is the payoff diagram for this straddle. Payoff 63 Straddle 70 S 63 77 T -7 3 Reverse Straddle: involves simultaneously selling a call option with • strike price X and selling a put option with strike price also X. In other words, it involves short positions in a call option and put option both with strike price X. Example (Reverse Straddle): Consider a portfolio with — a short position in a call option on a stock with a strike price of • X =$30andwithapriceof$4;and — a short position in a put option on the same stock with a strike price of X =$30and with a price of $4. Now let us find the payoff function for this portfolio as a function of ST , the stock price at expiration. If ST < $30, payoff is (30 ST )+4+4=ST 22 − − − If ST > $30 payoff is (ST 30) + 4 + 4 = 38 ST − − − Below is the payoff diagram for this reverse straddle. Payoff Reverse Straddle 8 2230 38 ST -22 4 Strangle: involves a simultaneous purchase of a put option with strike • price X1 and purchase of a call option with strike price X2 where X2 > X1. In other words, it involves long positions in a call option and put option where the strike price of the call is higher than the strike price of the put. Example (Strangle): Consider a portfolio with — a long position in a call option on a stock with a strike price of • X =$90andwithapriceof$6;and — a long position in a put option on the same stock with a strike price of X =$70and with a price of $4. Now let us find the payoff function for this portfolio as a function of ST , the stock price at expiration. If ST < 70, payoff is (70 ST ) 4 6=60 ST − − − − If 70 <ST < 90 payoff is 4 6= 10 − − − If ST > 90 payoff is (ST 90) 4 6=ST 100 − − − − Below is the payoff diagram for this strangle. Payoff 60 Strangle 60 S 70 90 100 T -10 5.
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