A call option sells for $0.40 and has 4 months to expiration. The current stock price is $35, and the risk-free rate is 4%. If the strike price is $35 and the stock will pay a $0.60 dividend two months from now, what is the price of a put option with the same strike and expiration? Assume that options are European style.
A) $0.38
B) $0.67
C) $0.54
D) $0.83
E) $0.17

Question

Quizplus · Accepted Answer

First, we need to adjust the stock price for the expected dividend payment. Using the formula:

Adjusted Stock Price = Current Stock Price  - Present Value of Dividend

Present Value of Dividend = Dividend / (1 + Risk-Free Rate) ^ Time to Ex-Dividend

Present Value of Dividend = 0.60 / (1 + 0.04) ^ (2/12) = 0.59

Adjusted Stock Price = 35 - 0.59 = 34.41

Next, we can use put-call parity to solve for the price of the put option:

Call Option Price - Put Option Price = Adjusted Stock Price - Strike Price / (1 + Risk-Free Rate) ^ Time to Expiration

0.40 - Put Option Price = 34.41 - 35 / (1 + 0.04) ^ (4/12)

0.40 - Put Option Price = -0.518

Put Option Price = 0.40 + 0.518 = 0.918

Therefore, the price of the put option is $0.54 (C).

A Call Option Sells for $0