1. A 10-month European call option on a stock is currently selling for $5. The s
ID: 2709601 • Letter: 1
Question
1. A 10-month European call option on a stock is currently selling for $5. The stock price is $64, the strike price is $60. The continuously-compounded risk-free interest rate is 5% per annum for all maturities. 1) Suppose that the stock pays no dividend in the next ten months, and that the price of a 10-month European put with a strike price of $60 on the same stock is trading at $1. Is there an arbitrage opportunity? If yes, how can you take advantage of it to make profit? 2) Now suppose instead that a dividend of $10 will be paid in six months. What price do you expect a 10-month European put with a strike price of $60 on the same stock to be trading at?
Explanation / Answer
The relationship is C + PV(k) = p+s Now we can check, 5+ PV(64) = 1+60 Or, 5 + 64 x 1/(1+5/1200)^10 = 1 + 60 or 5+61.39 = 61 therefore 66.39 > 61 So, there is an arbitage. Profit can be made by buying put option and sell the protective call
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