Stochastic volatility jump

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In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates.[1] This model fits the observed implied volatility surface well. The model is a Heston process for stochastic volatility with an added Merton log-normal jump. It assumes the following correlated processes:

[where S = Price of Security, μ = constant drift (i.e. expected return), t = time, Z1 = Standard Brownian Motion, q is a Poisson counter with density λ, etc.]