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Your adjusted scheme is correct. Basically, taking a maturity $T$, you can consider the forward price process $F_t^T = S_t e^{r(T-t)}$. You apply the Andersen scheme to $F_t^T$ and then note that \begin{align*} S_{t+\Delta} &= F_{t+\Delta}^T e^{-r(T-(t+\Delta))}\\ &=F_t^T \exp(\ \Box \ ) e^{-r(T-(t+\Delta))}\\ &=S_t e^{r(T-t)}\exp(\ \Box \ ) ...

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Yes interest rate is constant in the Heston Model. and we have \begin{align} \ln {{S}_{t+\Delta t}}=\ln {{S}_{t}}+r\Delta t+{{K}_{0}}+{{K}_{1}}{{v}_{t}}+{{K}_{2}}{{v}_{t+\Delta t}}+\sqrt{{{K}_{3}}{{v}_{t}}+{{K}_{4}}{{v}_{t+\Delta t}}}\,{{Z}_{v}} \end{align} where \begin{align} & {{K}_{0}}=-\frac{\kappa \rho \theta }{\sigma }\Delta ...

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I think there is something that has not been mentioned. "price" is used as the x variable instead of "change in price" or return. This could be a problem, as price itself is non stationary, causing problem to statistical properties. With that being said, correlation is an inflated indicator here, exaggerating their relations. In Heston's model, indeed, the ...

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