A stock sells for $60 per share, the annual standard deviation of returns on the stock is
Question:
A stock sells for $60 per share, the annual standard deviation of returns on the stock is estimated to be 45 percent, and the continuously compounded risk-free rate is 3 percent.
A. If the stock did not pay dividends, according to the Black-Scholes-Merton model, what would the price of a European call option with an exercise price of $62 and 1 month to expiration be?
B. Again, assuming no dividends, what would be the price of a European put option with an exercise price of $62 and 1 month to expiration?
C. Now assume that the stock pays a quarterly dividend of $0.75. Thus, based on the current $60 stock price, the annual dividend yield is 5% [note: continuously compounded dividend yield = ln(1.05) 0.0488]. Under these circumstances, according to the Black-Scholes-Merton model, what would the price of a European call option with an exercise price of $62 and 1 month to expiration be?
