In evaluating options on a stock, a two-step stock price tree and a corresponding put price tree have been constructed. Both trees are shown below. The time to expiration of the option is 0.5 years (each step, or ?t, is 0.25 years) and the risk-free rate is 1%. Assume that all options in the problem are European. (20 points)

Stock Price Tree				Put Price Tree
t = 0	t = 0.25	t = 0.5		t = 0	t = 0.25	t = 0.5
		64.20127				Puu
	56.65742				Pu
50		50		P0		Pud = 5
	44.12485				Pd
		38.94004				Pdd

What is the strike price of the put option? (2 points)

What are the values of Puu and Pdd? (4 points)

What is the risk-neutral probability? (Hint: you need to calculate u and d used in the formula from the stock price tree. d = 1/u) (4 points)

What are the values of Pu, Pd and P0 respectively (Hint: you can calculate Pu and Pd first and use the values of Pu and Pd to get P0) (6 points)

Price a call with a strike price of $50 using the stock tree (Hint: you can use the formula for two-step tree directly, meaning there is no need to get Cu or Cd. Just get C0 directly) (4 points)