Question

A call option with an exercise price of $40 and three months to expiration has a price of $4.10. The stock is currently priced at $39.80, and the risk-free rate is 4 percent per year, compounded continuously. What is the price of a put option with the same exercise price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Put option price= __________

Answer 1

NOTE: This put option needs to be priced using the put-call parity.

Strike Price = $ 40, Time to Expiry = 3-months or (3/12) = 0.25 years, Call Price = $ 4.1, Current Asset Price = $ 39.8 and the risk-free rate is 4 % per annum compounded continuously.

Let the put option price be $ P

Therefore, Call Price + Present Value of Strike Price = Put Price + Current Asset Price

4.1 + 40 / EXP(0.04 x 0.25) = P + 39.8

43.702 = P + 39.8

P = 43.702 - 39.8 = $ 3.90199 ~ 3.90