远期合约价格 $S_0-Ke^{-rT}$

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Prove that the price of a forward contract with strike $K$ at time 0 and expiry $T$ is

P = S_{0} - Ke^{-rT}

We assume no dividends and no repo rate

解析

无分红下，远期到期支付 $S_T-K$ 。用复制：

该组合到期净值为 $S_T-K$ ，与远期多头 payoff 相同，因此远期合约现值为

\boxed{P=S_0-Ke^{-rT}}.

若存在 repo/dividend，则相应调整 carry。