Rahul Sharma (Editor)

Stochastic volatility jump

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In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates. This model fits the observed implied volatility surface well. The model is a Heston process with an added Merton log-normal jump.

Model

The model assumes the following correlated processes:

d S = μ S d t + ν S d Z 1 + ( e α + δ ε − 1 ) S d q d ν = − λ ( ν − ν ¯ ) d t + η ν d Z 2 corr ⁡ ( d Z 1 , d Z 2 ) = ρ

[where S = Price of Security, μ = constant drift (i.e. expected return), t = time, Z1 = Standard Brownian Motion etc.]

References

Stochastic volatility jump Wikipedia
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