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・ Stochastic Processes and their Applications
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Stochastic volatility jump
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Stochastic volatility jump : ウィキペディア英語版
Stochastic volatility jump
In mathematical finance, the stochastic volatility jump (SVJ) model is suggested by Bates.〔(David S. Bates, "Jumps and Stochastic volatility: Exchange Rate Processes Implicity in Deutsche Mark Opitions", ''The Review of Financial Studies,'' volume 9, number 1, 1996, pages 69–107. )〕 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:
: dS=\mu S\,dt+\sqrt S\,dZ_1+(e^ -1)S \, dq
: d\nu =-\lambda (\nu - \overline) \, dt+\eta \sqrt \, dZ_2
: \operatorname(dZ_1, dZ_2) =\rho
(''S'' = what?, ''μ'' = what?, ''t'' = what? (time?), ''Z''1 = what? etc. )

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