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in university's lecture notes, from what I understand using the replication of portfolio principle to price derivates, the forward price of a contract K should be: $K = P_0(1+r)$ where $P_0$ is the spot price of the underlying and $r$ is the risk-free rate. However, with this definition, I do not see how the delta of a forwards contract = 1 (which is what many sources are claiming). Indeed, $\frac{dK}{dP_0}=1+r$ and this isn't 1 unless $r=0$. Can someone help clarify my misunderstanding of this issue? Many thanks

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I think your error is in confusing forward contract and forward price.

The forward price, with continuous interest rates, is $K=P_0e^{rT}$. It is a fixed parameter of your forward contract.

The forward contract value, on the other hand, is $V_t=P_t-Ke^{-r(T-t)}$. Its derivative w.r.t. the underlying is then indeed $dV_t/dP_t=1$.

HTH?

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  • $\begingroup$ An example would be the gross and net treasury futures basis wrt the underlying ctd price. $\endgroup$ – Edward Watson Jan 26 at 14:08

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