Imagine a financial market with one zero-coupon bond and one stock. The risk-free rate of interest over one period of time is r = 25% and the initial value of the stock is S₀ = $10. There are two possible states of the world at t = 1, say ?up? and ?down,? and the stock takes values

Now a call option on the stock is introduced into the market. Its payoff function is

with exercise price K = $13. Compute the risk neutral probabilities and the fair price C₀ of the derivative contract.

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(15 if w=1 S1(w) = 15 if w = Į. |C = max(Sj – K,0)