Question

The price of a non-dividend paying stock is $19 and the price of a three-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum. What is the price of a three-month European put option with a strike price of $20?

Answer 1

The price of the put option will be $1.80

Step-by-step explanation:

For finding the price of the put option given the price on the call option for the same underlying asset with the same strike price and price is given , we apply the Black-Scholes model of put-call parity to solve the price of the put option.

The put-call parity formular: p = K x e^(-rT) + c - St

where p = price of put of option

K = the strike price = $20

r = Applied Interest rate = 4%

T = time to maturity denominated in year = 3/12 = 0.25

c= call option price

St = spot price of underlying asset = $19

Thus p = 20 x e^(-0.04 x 0.25) + 1 - 19 = $1.80