A call option matures in six months. The underlying stock price is $37 and the stock's return has a standard deviation of 27 percent per year. The annual risk-free rate is 3.4 percent, compounded continuously. The exercise price is $0. What is the price of the call option?
A) $39.65
B) $32.14
C) $36.37
D) $32.23
E) $37.00

Question

Quizplus · Accepted Answer

Given that the exercise price is $0, the value of the call option is essentially the current stock price adjusted for the present value of money. Since the risk-free rate is 3.4% and the option matures in six months, we can calculate the present value of the stock price to find the price of the call option. However, in this specific scenario, because the exercise price is $0, the call option's value is essentially the current stock price itself, which is $37. This is because the option gives the right to buy the stock at $0, meaning the intrinsic value of the option is equal to the stock price itself, as there's no need to adjust for the time value of money in this unique case.

A Call Option Matures in Six Months