# Concept Question Regarding Short Rate Model

I have a conceptual question that needs help. Does anyone know whether the short rate model generate discount rate or forward rate?

• From a short rate model, you can bond price and then you can compute the forward rate. – Gordon Mar 14 '16 at 14:42

## 1 Answer

Which is the paper/book you are reading? It should be noted there. But basically in a short-rate model you have

1. a model for the short rate $r_t$
2. you can calculate zero-coupon bond prices from it by $P_T = E[\exp(-\int_{0}^T r_u du)]$
3. from these prices you can calculate the yield-to-maturity $Y_T$ which fulfills $$P_T =\exp( - Y_T T)$$ thus $Y_T = - \log(P_T)/T$.

From the yield-to-maturity of a zero bond you get the spot term structure and then by the usual calculations forward rates.

• @Quant2015 if you like the answer and if it helped you then you could accept it by clicking on the respective button ... – Ric Mar 16 '16 at 7:49
• so short rate is basically a forecasted discount rate in the short term? – Quant2015 Jul 11 '16 at 17:30