Heston

The model is

\[ \begin{aligned} dp_{t}&=\left(r+\left(\lambda_r-\frac{1}{2}\sigma_{t}^{2}\right)\right)dt +\sigma_{t}dW_{t}^{r},\\ d\sigma_{t}^{2}&=\kappa\left(\mu-\sigma_{t}^{2}\right)dt +\eta\sigma_{t}dW_{t}^{\sigma}, \end{aligned} \]

with \(p_{t}=\log S_{t}\), and \(Corr\left[dW_{s}^{r},dW_{s}^{\sigma}\right]=\rho\), or in other words

\[ W_{t}^{\sigma}=\rho W_{t}^{r}+\sqrt{1-\rho^{2}}W_{t}^{v}. \]

Feller condition for positivity of the volatility process is \(\kappa\mu>\frac{1}{2}\eta^{2}\).

See the API reference for HestonParam and Heston.