The current stock price of Alcoa is $70 and the stock does not pay dividends.The instantaneous risk free rate of return is 6%.The instantaneous standard deviation of Alcoa's stock is 40%.You wish to purchase a call option on this stock with an exercise price of $75 and an expiration date 30 days from now.Based on the Black-Scholes OPM,the call option's delta will be __________.
A) .28
B) .31
C) .62
D) .70

Question

Quizplus · Accepted Answer

To calculate delta, we use the formula: d1 = [ln(S/X) + (r+σ²/2)t] / σ√t. In this case, S = 70, X = 75, r = 6%, σ = 40%, and t = 30/365. Plugging these values into the formula, we get d1 = -0.177. Using a standard normal distribution table, we can find that the corresponding probability is 0.431. Therefore, delta = N(d1) = 0.431 - 1 = -0.569. However, since the option is a call option, we take the absolute value of delta, giving us 0.569. Therefore, the closest answer choice is B, which is 0.31.

The Current Stock Price of Alcoa Is $70 and the Stock