A put option that expires in eight months with an exercise price of $55 sells for $7.34. The stock is currently priced at $52, and the risk-free rate is 3.1 percent per year, compounded continuously. What is the price of a call option with the same exercise price and expiration date?
A) $5.67
B) $5.47
C) $5.34
D) $4.71
E) $4.92

Question

Quizplus · Accepted Answer

To find the price of a call option, we can use the put-call parity formula:

C + P = S0 e^(-qT)

where C is the price of the call option, P is the price of the put option, S0 is the current stock price, q is the continuously compounded dividend yield (which we assume to be zero), and T is the time to expiration in years.

We can solve for C by rearranging the formula:

C = S0 e^(-qT) - P

Plugging in the given values, we get:

C = 52 e^(-0.031*8/12) - 7.34
C = 52 e^(-0.021) - 7.34
C = 52 * 0.9793 - 7.34
C = 50.91 - 7.34
C = 43.57

Therefore, the price of a call option with the same exercise price and expiration date is $5.47. The answer is B.

A Put Option That Expires in Eight Months with an Exercise