Formalize: Forward Contracts on Investment Assets with Known Yield
(Continuous Payment - continued)

Value of a forward contract on assets with known yield

Consider an existing forward contract on an asset with known yield, δ:
T = a maturity date
F₀ = delivery price of the existing position, = S₀e^{(r-δ)(T- 0)}
What is the value of a long forward contract at t = t1? Short forward contract?

The answer to this question is:

F_t1 = forward price of the contract prevailing at t₁ > 0
      =S_t1e^{(r-δ)(T- t1)}

Long: V_t1  = (F_t1 – F₀ )e^–r(T-t1) = S_t1e^{- δ (T-t1)} – F₀ e^–r(T-t1)
Short: V_t1 = (F₀ – F_t1 )e^–r(T-t1) = F₀ e^–r(T-t1) – S_t1e ^{- δ (T-t1)}