There is a long forward contract on a single, non dividend paying, stock with price S t at time t The payoff at time T is S T F 0,T where F 0,T is the current forward price (t 0) Now consider a one step binomial tree where there is one time step to maturity, the current stock price S 0 can increase to S T uS 0 or down to S T dS 0 at time T The continuously compounded rate over the period is r 1) what current positions (t 0) in the stock and risk free investment will replicate the payoff of the long forward contract for any F 0,T What is the replicating portfolio 2) what is the current value of the forward contract

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Question: There is a long forward contract on a single, non-dividend paying, stock with price S t at time t. The payoff at time T is

There is a long forward contract on a single, non-dividend paying, stock with price S_t at time t. The payoff at time T is S_T - F_0,T where F_0,Tis the current forward price (t = 0).Now consider a one-step binomial tree where there is one time step to maturity, the current stock price S₀ can increase to S_T = uS₀ or down to S_T = dS₀ at time T.The continuously compounded rate over the period is r.

1) what current positions (t = 0) in the stock and risk-free investment will replicate the payoff of the long forward contract for any F_0,T ? What is the replicating portfolio?

2) what is the current value of the forward contract?

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