Referencesīates, D., Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options, The Review of Financial Studies, Vol. $$ \begin\), is mean reverting with mean reversion level \(\theta\), mean reversion strength \(\kappa\) and constant volatility \(\sigma\). The stochastic differential equations (SDE) for the asset level and the variance under the risk neutral measure are given by Bates (1996) was one of the first to describe this particular combination of models. The stochastic volatility in Heston's model is a mean-reverting square-root process. The jumps are assumed to be independent from the diffusion. Merton's model is based on the classic Black-Scholes model but extended to include discontinuous asset returns. Here, as an example, we present the basic case of a combination of Merton's jump diffusion model and Heston's stochastic volatility model. The advantage of the model is that it is possible to replicate stylized facts such as heavy tails and volatility clustering and mean reversion, negative correlation between returns and volatility, and sudden large movements in the price of the asset. ![]() Stochastic Volatility Jump Diffusion (SVJD) is a type of model commonly used for equity returns that includes both stochastic volatility and jumps.
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