Prepaid forward contract ($V_t=S_t{e}^{-q(T-t)}$)

A prepaid forward pays for delivery of an asset at a future time entirely in advance. In the Black-Scholes model with deterministic continuous dividend yield $q$, one share delivered at $T$ costs the displayed amount at $t$. Reinvesting the dividends on $e^{-q(T-t)}$ shares replicates one terminal share. An ordinary forward contract instead has no initial payment and a delivery payment fixed in advance; at constant interest rate $r$ its fair delivery price is $S_t{e}^{(r-q)(T-t)}$.