Stochastic volatility jump

Summary

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 is the price of security, μ is the constant drift (i.e. expected return), t represents time, Z1 is a standard Brownian motion, q is a Poisson counter with density λ.

References

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  1. ^ David S. Bates, "Jumps and Stochastic volatility: Exchange Rate Processes Implicity in Deutsche Mark Options", The Review of Financial Studies, volume 9, number 1, 1996, pages 69–107.