Given that $P(0,T)=e^{-RT}$, how does one get the formula for the instantaneous forward rate below? Specifically, how does one get to the partial derivative in the formula?

I'm sure the answer is obvious but I haven't been over my calculus in a while.

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1 Answer 1


You can start with $$P(t,T)=exp({-\int_t^T f_t(u).du})$$ then take derivative wrt to T $$R_F(0,T)=f_0(T)=-\frac{\partial} {\partial T}{ ln(P(0,T))} $$


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