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I'm wondering if there is a way to work out the formula for the price of the zero-coupon bond using the Vasicek's model (P measure). I have tried to find reference on it but could not, I don't know if it is possible.

I know that under the Q measure, the zero-coupon bond price would be

$P(t,T)= A(t,T)e^{r(t)B(t,T)}$

where

$A(t,T)=exp\{(b - \frac{\sigma^2}{2a^2})(B(t, T)-T+t)-\frac{\sigma^2}{4a}B^2(t,T)\}$

$B(t,T)=\frac{1-e^{-a(T-t)}}{a}$

I have a P-measure model $dr_t=(a(b-r_t)-\lambda\sigma)dt+\sigma dW^\mathbb{P}_t$, where the $\lambda$ is the risk premium. I don't know if it is possible to do it or that I'm just heading the wrong way and should instead work with the Q-measure ZCB formula.

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