a) Explain how some of the assumptions of the Black-Scholes-Merton model (BSM) can be relaxed.

b) Examine if (i) eS and (ii) e(2S+1) could be the prices of a traded derivative security.

c) A stock price is currently $60. Assume that the expected return from the stock is 25% and its volatility is 35%. What is the probability distribution for the rate of return (with continuous compounding) earned over a four-year period?

d) (i) Use the BSM model to find the theoretical value of a European put option on a non-dividend- paying stock when the stock price is 50, the strike price is 50, the (continuously compounded) risk-free interest rate is 10% per annum, the volatility is 30% per annum, and the time to maturity is three months.

(ii) At what price of the stock would the buyer of the put option break even?

(iii) How would you value the put option in (i) if a dividend of 1.50 was expected in two months?