Given the following: Current stock price = $80 Standard deviation = 30% Strike p

Question

Given the following: Current stock price = $80 Standard deviation = 30% Strike price = $85 Time to expiry = 6 months Risk-free rate = 5% Use the Black-Scholes Option Pricing Formula to calculate the value of a European call option. What is the value of a European put option, using the same parameters that are given at the top of this page? What is the exercise value and what is the time premium of the call option in part (a)? At what value of stock price would the time premium of the call option in part(a) be at a maximum? Is it possible for an American option to worth less than a corresponding European option?

Explanation / Answer

Input Data Stock Price now (P) 80 Exercise Price of Option (EX) 85 Number of periods to Exercise in years (t) 6 Compounded Risk-Free Interest Rate (rf) 5.00% Standard Deviation (annualized s) 30.00% Output Data Present Value of Exercise Price (PV(EX)) 62.9695 s*t^.5 0.7348 d1 0.6932 d2 -0.0417 Delta N(d1) Normal Cumulative Density Function 0.7559 Bank Loan N(d2)*PV(EX) 30.4382 Value of Call 30.0338 Value of Put 13.0033

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