A non-dividend paying stock currently trades for $50 and has an annualised return volatility (standard deviation) of 20%. Given that the continuously compounded risk-free rate of return is 4% p.a., complete the following:

a. Using a two-step binomial tree, price the European put option on the stock when the put has an exercise price of $55 and 3 months to maturity. (4 marks)

b. Using the Black-Scholes-Merton Model, price the put option from part a) above. (3 marks)

c. What is the delta of the put option from part b) under the Black-Scholes-Merton Model? How can a long position in 1000 of these put options be made delta neutral using the underlying stock? What would you have to do to delta hedge the position over the next 6 months? (3 marks)

d. Explain the concept of implied volatility and how it can be a useful measure of market expectations. (3 marks)