Assume the Black-Scholes framework. You are given:

(i) The current stock price is 100.

(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 2.5%.

(iii) The continuously compounded expected rate of return on the stock is 6%.

(iv) The stock’s volatility is 30%.

Calculate:

(a) The probability that a 3-year at-the-money European put option on the stock is exercised 

(b) The 95% percentile of the 3-year stock price 

(c) The expected 3-year stock price 

(d) The expected 3-year stock price, given that the put option in (a) pays off at maturity 

(e) The variance of the 3-year stock price