QUESTION 3 (4 + 2 + 5 + 2 + 2 = 15 marks) Consider an institution that has just sold to a client an at-the-money American put option with a 6- month maturity. The underlying is a non-dividend paying stock priced at $30. Assuming a continuously compounded risk-free rate of 6% p.a. and stock price movements of +/- 10% each period

a) Price the option using a three-period binomial option pricing model. [4 marks]

b) Given the pricing model you used in part a), when should the client exercise the option?Why? [2 marks]

c) Show how the institution would hedge their exposure to the stock if the stock price fell every period. [5 marks]

d) Explain the intuition behind the evolution of the hedging strategy over the life of the hedge. [2 marks]

e) Is the price for an otherwise equivalent European put likely to be higher or lower than the price of the American put? Why? [2 marks]