Consider a 3-month put option on a stock. The current stock price is $100; and the stock pays no dividend during the next 3-month. You estimate that the stock volatility is 20% per annum. The option has a strike price of $105. Risk free interest rate is 5%. You use a 2-step CRR binomial model to price this option.

a) What is the risk neutral probability of stock price moving up in any one time step?

b) Suppose the option is a European put option. Use the binomial tree below to compute the option price.

c) Suppose the option is an American put option. Use the binomial tree below to compute the option price.

d) Suppose the option is an Asian option, where the strike price is average stock price over life of the option. Use the binomial tree below to compute the option price.

Please show calculate process.