4. (a) Explain the Binomial model for the evolution of a stock

price for t = 0,1,2 when you are given probabilities

for the up state and (1 ) for the down state. Show how

to compute the probabilities for all the states at t = 2.

(b)

For the case of t = 0,1 explain how you can use a

portfolio of a stock and bond to replicate a call option

payoff.

(c)

For t =0,1 show how you can find the price for the two ArrowDebreu securities, and how they have the same properties as

probabilities.

(d)

Now using your answers to parts (a) and (c) show how you can

value (at t = 0) any cash flow at t = 2. (Hint: recall the

properties of AD prices and the probabilities derived in (a).)

(e) Outline how this simple model can be generalized, and

converges to the Black-Scholes call option pricing model.