Question 4

Consider an option on a non-dividend-paying stock where the stock price is $60, the exercise or strike price is $54, the risk-free interest rate is 1% per annum with continuous compounding, the volatility is 35% per annum, and the time to maturity is 6 months. Assume that the stock price follows a Geometric Brownian Motion.

(a)Using the Black-Scholes-Merton model, compute the price of the option specified above if it is a European put option.

(b)Without using the Black-Scholes-Merton model, find the price of the corresponding European call option with the same strike price and maturity.

(b)If the actual price of the put option in the market is $0.10 higher than the value you computed in (a), what can you say about the implied volatility in relation to the 35% volatility stated in the question? Is the implied volatility higher than, lower than or equal to 35%? Briefly explain your answer.