Problem
In this question, the instantaneous risk free rate r follows an arbitrary stochastic process. Consider a forward contract, entered into at date 0, to buy a non-dividend paying underlying at date T.
i. Find the marked-to-market value Vt of this contract at time t < T in terms of the spot price at date t, St, and the forward price at date 0, F0.
ii. Now suppose that St = S0, i.e. the price of the underlying at date t is the same as its price at date 0. Find a condition on zero-coupon prices under which Vt = 0. Interpret.