The current price of a non-dividend stock is $55. The stock price is expected to either rise 20% or fall 20% each year and the continuously compounded risk-free rate is 5% p.a. The option has 2 years to expiration and the exercise price of the option is $53.

a. Using the binomial option pricing model by dividing the life of the option into two intervals of length one-year each, what is the value of a European and American put option on the stock?

b. An investor buys the above American put option at todays fair value. Calculate the number of shares the investor needs to trade to hedge her option position according to the delta-neutral approach. Assume an option is for 1 share. Clearly state whether the investor needs to buy or sell the shares.