As in previous question mentioned, I attended a course in interest rate theory (I'm studying math). Now I have a question how one calculate this prices in reality. Suppose we assume a simple model for our interest rate, let's say the instantenous spot rate is modeled by the Vasicek model. Hence $r(t)$ has is a Gaussian process. The arbitrage free bond prices are given by
where $Q$ is a equivalent (local) martingale measure. How do you compute this computationally? The conditional expectation is random variable, even more you integrate the Gaussian process, so how do you proceed in reality to compute such an conditional expectation?
Thanks in advance for your help