Question #40:

a) You are asked to value a European call option on a stock. The stock price is $80, the time to maturity is 1 year, the risk-free rate is 5% per annum, compounded continuously, the exercise price is $85, and the stock return volatility is 25%. Dividends of $1 are expected in 3 months, 6 months and 9 months. Calculate the price of the option.

b) What if the call option in a) is American? What is its price then?

c) What if the option in a) is a European put option? What is its price then? Calculate its price using both the Black-Scholes-Merton model and put-call parity. Compare the two prices calculated and explain any discrepancies between them.