# Delta of a forwards contract

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

## 1 Answer

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?

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