Exam MFE/3F Sample Questions and Solutions April 6, 2010 1 1. Consider a European call option and a European put option on a nondividend-paying stock. You are given: (i) The current price of the stock is 60. (ii) The call option currently sells for 0.15 more than the put option. (iii) Both the call option and put option will expire in 4 years. (iv) Both the call option and put option have a strike price of 70. Calculate the continuously compounded risk-free interest rate. (A) 0.039 (B) 0.049 (C) 0.059 (D) 0.069 (E) 0.079 2 Answer: (A) Solution to (1) The put-call parity formula (for a European call and a European put on a stock with the same strike price and maturity date) is C  P  F0,PT ( S )  F0,PT ( K )  F0,PT ( S )  PV0,T (K)  F0,PT ( S )  KerT = S0  KerT, because the stock pays no dividends We are given that C  P  0.15, S0  60, K  70 and T  4. Then, r  0.039. Remark 1: If the stock pays n dividends of fixed amounts D1, D2,…, Dn at fixed times t1, t2,…, tn prior to the option maturity date, T, then the put-call parity formula for European put and call options is C  P  F0,PT ( S )  KerT  S0  PV0,T(Div)  KerT, n  rt where PV0,T(Div)   Di e i is the present value of all dividends up to time T. The i 1 difference, S0  PV0,T(Div), is the prepaid forward price F0P,T ( S ) . Remark 2: The put-call parity formula above does not hold for American put and call options. Fo ...
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