Value of a Forward contract at an intermediate time
Suppose we hold a forward contract on a stock with expiration 6 months from now. We entered into this contract 6 months ago so that when we entered into the contract, the expiration was T=1 year.
The stock price$ 6 months ago was S0=100, the current stock price is 125 and the current interest rate is r=10% compounded semi-annually. (This is the same rate that prevailed 6 months ago.) What is the current value of our forward contract?
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Your formula is incorrect.
The fair future value of a stock (with interest compounding semi-anually) is
F = S * (1+r/2)^(2t)
The fair future value when you purchased the forward was:
100 * (1+0.05)^2 = 110.25
The current fair value of the forward that expires in 6 months is
125 * (1+0.05)^1 = 131.25
So the current value of the forward is
131.25 - 110.25 = 21
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