= 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. i) Construct the tree of forward prices F(t,T) Soe"(T-t) for a forward contract on the stock, with maturity T = 27. ii) Show that at each node in the tree times t=0,1) the forward prices satisfy the martingale condition (1) F(t,T) = EQ[F(t +T,T)] = pF(t +T,T; up) + (1 - p)F(t + T; down) ert -d = u-d with the usual tree probability p 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 > t (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. i) Construct the tree of forward prices F(t,T) Soe"(T-t) for a forward contract on the stock, with maturity T = 27. ii) Show that at each node in the tree times t=0,1) the forward prices satisfy the martingale condition (1) F(t,T) = EQ[F(t +T,T)] = pF(t +T,T; up) + (1 - p)F(t + T; down) ert -d = u-d with the usual tree probability p 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 > t (2) F(t1;T) = EQ[F(t2;T)] This martingale property holds also for futures contracts