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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.
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