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?

The price of the put option will be $1.80

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