Given Vasicek model in for short rate
\begin{equation} dr=k(a-r)dt+\sigma dW_{t} \end{equation}
where $k,a,\sigma$ positive constant and $W_{t}$ standard BM under $Q$. Suppose there is a call option
\begin{equation} X=max[p(T_{0},T)-k,0] \end{equation}
where $p(t,T)$ is price of the a T-bond at $t$ and $T_{0}<T$.
By definition a replication of this claim is a value process which converges a.s in probability to $X$. Suppose
$V^{h}_{t}=h^{T_{0}}p(t,T_{0})+h^{T}p(t,T)$
in other words a portfolio of T-bond and T_{0}-bond. I know that $h^{T_{0}}$ and $h^{T}$ can be found as standard normal distribution in the same manner as classic pricing formula for call option.
\begin{equation} h^{T}=\Phi(d_{1}) \end{equation}
\begin{equation} h^{T_{0}}=\Phi(d_{2}) \end{equation}
So that is not an issue but, how do one show that this actually converges in probability to $X$?