I would like to compute $ E[X_{T}]$ and $Var[X_{T}]$ in the Jacobi model, where the Dynamics are given as \begin{align} dY_{t}&=\kappa(\theta-Y_{t})dt+\sigma\sqrt{Q(Y_{t})}dW_{1t}\\ dX_{t}&=(r-\delta-0.5Y_{t})dt+\rho\sqrt{Q(Y_{t})}dW_{1t}+\sqrt{Y_{t}-\rho^{2}Q(Y_{t})}dW_{2t} \end{align} where $W_{1t}$ and $W_{2t}$ are two correlated Brownian motions and $Q(Y_{t})=\frac{(Y_{t}-y_{min})(y_{max}-Y_{t})}{(\sqrt{y_{max}}-\sqrt{y_{min}})^2}$. The parameters are given as: $\kappa=0.5=-\rho, r=\delta=X_{0}=0, \theta=Y_{0}=0.04, y_{min}=10^{-4}, y_{max}=0.08$ and $\sigma=1$ and $T=1/12$.


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