10.A two-step binomial tree is used to value an American put option on one share of ABC stock. The strike price is $150 and the expiration date is in 6 months. Each step is 3 months. Todays spot price of one share of ABC stock is $155. The US risk free rate is 5%, and the stock does not pay any dividend. The volatility of ABC stock is 30% per annum. a) What are the proportional up movement, u, and the proportional down movement, d? b) What is the probability of an up movement, p? c) What is todays price of the American put option ? Show your work in deriving the trees of stock and option prices.