Question

Question 1 Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Answer the following questions using the Black-Scholes option pricing model.

a) What is the price of the option if it is a European call?

b) What is the price of the option if it is an American call?

c) What is the price of the option if it is a European put?

d) Verify that put–call parity holds.

Answer 1

a) and b)

c)

d)

As per put call parity

Call price + PV of exercise price = Spot price + Put price
2.524 + 29 X e^(-0.05X0.33333) = 30 + Put price
Put price = 1.05

Hence proved