Thread: Vasicek model

Hi can you please help me with this problem,

For the Vasicek interest rate model with short rate process dr_t = K(θ-r_t)dt + σ dW_t, show that the bond price B(t,T,r) can be found as B(t,T,r)=exp[A(t,T)r_​t+Z(t,T)] for deterministic functions A(t,T) and Z(t,T). Find A(t,T) and Z(t,T).

Hey nirmal019.

You need to use the generalized form of Ito's lemma to get the integral portion for the non-random and random components. Do you know these identities? (I'm sure you have been given these by your lecturer/professor).