What is the value of a call given the Black-Scholes model and the following information? Stock price = $44,Exercise price = $40,Time to expiration = .75,Risk-free rate = 4.5%,Standard deviation = 25%,N(d₁)= .759395,and N(d₂)= .687172. A)$2.03 B)$4.86 C)$6.84 D)$8.81 E)$9.27

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Quizplus · Accepted Answer

The value of a call option in the Black-Scholes model is given by the formula: 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 values from the cumulative normal distribution function for d1 and d2 respectively, X is the exercise price, r is the risk-free interest rate, t is the time to expiration, and e is the base of the natural logarithm. Given S0 = $44, X = $40, r = 4.5% or 0.045, t = 0.75, N(d1) = 0.759395, and N(d2) = 0.687172, substituting these values into the formula gives the value of the call option. The correct calculation leads to a value of $6.84, which matches option C.

What Is the Value of a Call Given the Black-Scholes