FBE459_Homework3_solutions - UNIVERSITY OF SOUTHERN...

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UNIVERSITY OF SOUTHERN CALIFORNIA MARSHALL SCHOOL OF BUSINESS FBE 459 Financial Derivatives (P. Matos – Spring 2011) Homework 3 (Solutions): Q.1. The price of a non-dividend paying stock is $18 and the price of a 3-month European call option on the stock with a strike price of $20 is $1. The risk-free is 4% per annum. a. What should be the price of a 3-month European put option with a strike price of $20? Solution: From the put-call parity: p + S = c + Ke -r.T p + 18 = 1 + 20.e -0.04*(1/4) p = 2.801 b. Explain what arbitrage opportunity exists if the European put option price is $2? Solution: The “buy low, sell high” arbitrage strategy for this case is: 2 + 18 < 1 + 20.e -0.04*(1/4) “buy low” “sell high” (long put & stock) (short call & K in bonds) today at expiration (T) (t=0) S T <K S T >K "buy low" buy put -2 (20-S T ) 0 buy stock -18 S T S T "sell high" sell call 1 0 -(S T -20) borrow K at r 19.801 -20 -20 profits 0.801 0 0 Q.2. The stock of the pharmaceutical company is trading at $40. There are currently two options trading: a European call option with a strike price of $45 and a European put option with the same strike price of $45. Both options have the same maturity of 1 year. Currently the interest rate is at 9.3% per year. a. The call costs $3. What needs to be the price of the put? Solution: From the put-call parity: p + S = c + Ke -r.T p + 40 = 3 + 45.e -0.093*(1) p = 4
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b. Suppose you want to bet that the stock price will not move much around the current stock price. Using the put and call options available, how would you construct an option strategy to profit from your market view? Explain and describe the schedule of payoffs. What’s your maximum potential gain and maximum loss in this strategy? Solution: You should short (write) both a call and put options. This type of trading strategy is known as a “short straddle”. The trader position payoff is: S T <45 S T >45 SHORT Put option (K=$45) -[45 - S T ] 0 SHORT Call option (K=$45) 0 -[S T – 45] Options premiums +7 +7 TOTAL S T -38 52-S T Payoff +$7 +$4 +$3 $45 S The maximum potential gain is $7 (the sum of the option premiums) The maximum potential loss is unlimited, if S goes up !
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This note was uploaded on 04/20/2011 for the course FBE 459 taught by Professor Matos during the Spring '08 term at USC.

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FBE459_Homework3_solutions - UNIVERSITY OF SOUTHERN...

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