A stock price follows geometric Brownian motion with an expected return (µ) of 15% and a volatility (σ) of 30%.
The current price is $45. (Tip: make use of the ln(ST) distribution)
(a) What is the probability that a European call option on the stock with an exercise price of $50 and a maturity date in six months will be exercised?
(b) What is the probability that a European put option on the stock with the same exercise price and maturity will be exercised?