Derive instantaneous forward rate - Quantitative Finance Stack Exchange most recent 30 from quant.stackexchange.com 2019-08-17T13:43:20Z https://quant.stackexchange.com/feeds/question/11327 http://www.creativecommons.org/licenses/by-sa/3.0/rdf https://quant.stackexchange.com/q/11327 1 Derive instantaneous forward rate mathjacks https://quant.stackexchange.com/users/2812 2014-05-17T00:28:48Z 2014-05-17T02:11:17Z <p>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?</p> <p>I'm sure the answer is obvious but I haven't been over my calculus in a while.</p> <p><img src="https://i.stack.imgur.com/Z8Dcf.png" alt="enter image description here"></p> https://quant.stackexchange.com/questions/11327/-/11329#11329 3 Answer by DerekT for Derive instantaneous forward rate DerekT https://quant.stackexchange.com/users/8076 2014-05-17T01:35:29Z 2014-05-17T02:11:17Z <p>You can start with $$P(t,T)=exp({-\int_t^T f_t(u).du})$$ then take derivative wrt to T $$R_F(0,T)=f_0(T)=-\frac{\partial} {\partial T}{ ln(P(0,T))}$$</p>