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. b) Given the pricing model you used in part a), when should the client exercise the option?Why? c) Show how the institution would hedge their exposure to the stock if the stock price fell every period. d) Explain the intuition behind the evolution of the hedging strategy over the life of the hedge. e) Is the price for an otherwise equivalent European put likely to be higher or lower than the price of the American put? Why?