Assume a stock price of $31.18, risk-free rate of 3.6 percent, standard deviation of 44 percent, N(d₁) value of .62789, and an N(d₂) value of .54232. What is the value of a 3-month call option with a strike price of $30 given the Black-Scholes option pricing model?

Question

Quizplus · Accepted Answer

The value of a call option using the Black-Scholes model is given by: C = S0*N(d1) - X*e^(-rt)*N(d2), where C is the call option price, S0 is the current stock price, N(d1) and N(d2) are the cumulative distribution functions for d1 and d2, X is the strike price, r is the risk-free rate, t is the time to expiration in years, and e is the base of the natural logarithm. Plugging in the given values: C = 31.18*0.62789 - 30*e^(-0.036*0.25)*0.54232 = 19.57 - 16.12 = $3.45.

Assume a Stock Price of $31