Assume that the current price of DEY stock is $25,that a 6 month call option on the stock has a strike or exercise price of $27.50,the risk free rate is 4%,and that you have calculated N(d₁)as .5476 and N(d2)as .4432.Use the Black-Scholes model to calculate the price of the option.

Question

Quizplus · Accepted Answer

The price of the call option can be calculated using the Black-Scholes formula:
C = S*N(d1) - X*e^(-rt)*N(d2)
where C is the price of the call option, S is the current stock price, X is the exercise price, r is the risk-free rate, t is the time to expiration, and N(d1) and N(d2) are standard normal cumulative distribution functions evaluated at d1 and d2, respectively.

d1 = [ln(S/X) + (r + σ^2/2)*t]/(σ*sqrt(t))
= [ln(25/27.5) + (0.04 + 0.25^2/2)*0.5]/(0.25*sqrt(0.5))
= -0.3683

d2 = d1 - σ*sqrt(t)
= -0.3683 - 0.25*sqrt(0.5)
= -0.7483

N(d1) = 0.3524
N(d2) = 0.2269

C = 25*0.3524 - 27.5*e^(-0.04*0.5)*0.2269
= $1.74

Therefore, the best choice is A) $1.74.

Assume That the Current Price of DEY Stock Is $25,that