# Deriving the yield curve from the HJM dynamics

If I know that my model follows a no-arbitrage HJM model: $$df(\tau) = \left(\sigma(\tau)\int_0^{\tau}\sigma(u)du\right)dt +\sigma(\tau)dW_{\tau}$$ (where $\tau:=T-t$, the time until maturity $T$ of a Bond and) $\sigma$ a process adapted to $W_{\star}$'s filtration.

How do we derive the yield curve for such a model? That is the models I see all have deterministic yield curve, is this the expectation of the above SDE?

• What do you mean yield curve, that is, specifically, what quantity you want to derive? – Gordon Mar 12 '16 at 21:32
• I want the forward rate curve's solution; ie I'm looking for a solution to the above SDE – AIM_BLB Mar 12 '16 at 21:39
• Other than $f(\tau) = \frac{1}{2}\big(\int_0^{\tau}\sigma(s) ds\big)^2 + \int_0^{\tau}\sigma(s) dW_s$, for your equation, I do not see any more compact analytical solution. – Gordon Mar 14 '16 at 18:48