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Equity Forward Contract

A commitment to buy or sell an equity at a fixed price F₀(T) at a future date T, priced to have zero value at inception.

The no-arbitrage forward price is F₀(T) = (S₀ − PV(Dividends)) × e^(rT). The cost-of-carry framework: the forward buyer avoids the opportunity cost of owning the stock (financing) but also forgoes dividends. Mid-life value for the long position: V_t = S_t − PV_t(remaining dividends) − F₀(T)·e^(−r(T−t)). A key insight: since the forward is priced at zero NPV at inception, any subsequent price change is reflected in the mark-to-market value V_t.

Formula
F0(T)=(S0PV(div))erTF_0(T) = (S_0 - PV(\text{div})) \cdot e^{rT}