Consider a 2-period binomial tree model for a stock with spot price So, volatility o and risk-free interest rate r. Denote the time step of the tree t. Construct the tree of prices for a (long) forward contract on the stock, with forward price K and maturity T = 27. Recall the distinction between the price of a forward contract and the forward price. i) Using the payoff the forward contract fi = Si- K at maturity, compute by backwards recursion the price of the forward contract at all previous nodes of the tree. ii) What should the forward price K be such that the value of the forward contract at time zero vanishes? Compare the result with the arbitrage price F(T) = Soe2rt. This would be the forward price if we entered the forward contract at time 0. iii) Denote K, K the forward prices at time t in the tree, corresponding to the two nodes. Show that their risk-neutral expectation is (1) EQ[K1] = puk + pak? = K This illustrates the martingale property of the forward price: the forward price at time ti is equal to the expectation in the risk-neutral measure of the forward price at any later time t2 > ti (2) F(t1:T) = Eq[F(t2;T)] This martingale property holds also for futures contracts Consider a 2-period binomial tree model for a stock with spot price So, volatility o and risk-free interest rate r. Denote the time step of the tree t. Construct the tree of prices for a (long) forward contract on the stock, with forward price K and maturity T = 27. Recall the distinction between the price of a forward contract and the forward price. i) Using the payoff the forward contract fi = Si- K at maturity, compute by backwards recursion the price of the forward contract at all previous nodes of the tree. ii) What should the forward price K be such that the value of the forward contract at time zero vanishes? Compare the result with the arbitrage price F(T) = Soe2rt. This would be the forward price if we entered the forward contract at time 0. iii) Denote K, K the forward prices at time t in the tree, corresponding to the two nodes. Show that their risk-neutral expectation is (1) EQ[K1] = puk + pak? = K This illustrates the martingale property of the forward price: the forward price at time ti is equal to the expectation in the risk-neutral measure of the forward price at any later time t2 > ti (2) F(t1:T) = Eq[F(t2;T)] This martingale property holds also for futures contracts