Question

A call option is currently selling for $4.5. It has a strike price of $75 and seven months to maturity. The current stock price is $77, and the risk-free rate is 4.4 percent. The stock will pay a dividend of $2.2 in two months. What is the price of a put option with the same exercise price? (Round your answer to 2 decimal places. Omit the "$" sign in your response.) Price of a put option $

Answer 1

As per Call Put Partiy

Dividend * e^(-r*t) +Strike Price * e^(-r*t) + Premium on Call Option = Current Value of Stock + Premium on Put Option

where r is the risk free rate of return i.e. 0.044

t is the time period 7 / 12 = 0.58333333333

t for dividend is 2 / 12 = 0.16666666666

2.2 * e^(-0.044 * 0.16666666666*)+75 * e^(-0.044*0.58333333333) + 4.50 = 77 + P

2.2 * 0.99269348995 + 75 * 0.97465992211 + 4.50 = 77 + p

2.18392567789 + 73.0994941582 + 4.50 = 77 + P

79.78 = 77 + P

P = 2.78