The price of a European call option on a stock with a strike price of $50 is $6.
ID: 2721752 • Letter: T
Question
The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $2 is expected in six months. What is the fair price of a one-year European put option on the stock with a strike price of $50? If the put is currently selling for $6, what should an investor do (describe the steps to take advantage of any potential arbitrage opportunity and calculate the arbitrage profit if any)?
Explanation / Answer
Answer: Put-call parity is c+Ke -rT =p+S 0 D .
In this case K =50, S 0 =51, r =0.06, T =1, and c =6. The present value of the dividend, D , is 2×e 0.06×0.5 =1.94.
It follows that p =6+50e -0.06×1 (51-1.94) =4.03
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