Heston Model

Stochastic Differential Equation used in Finance, defined by

$$\begin{array}{rl}d{S}_t& =S_t\sqrt{V_t}d{W}_t\\ d{V}_t& =\lambda \left(\theta -V_t\right)dt+\lambda \nu \sqrt{V_t}d{B}_t\\ ⟨d{W}_t,d{B}_t⟩& =\rho dt\end{array}$$

Where:

• $W_t$, $B_t$ are standard Wiener Processes
• $\lambda$, $\rho$, $\mu$, $\theta \in \mathbb{R}$ are constants
• $S_t,V_t$ are Semimartingales representing the stock price and volatility, respectively

Further reading: Intro to the Rough Heston Model