A stochastic volatility model with jumps

2006/03/22 by Youssef El‐Khatib, Youssef El-Khatib, El-Khatib, Youssef
Economics, Econometrics and Finance · Mathematics · Social Sciences · #60H07 #91B24 #91B26 #91B28 #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60H07 #msc:91B24 #msc:91B26 #msc:91B28 #q-fin.PR

paper · pdf · doi:10.48550/arxiv.math/0603527

openalex publication_date 2006/03/22 · arxiv created 2011/10/28 · arxiv updated 2011/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in infinitely many equivalent martingale measures. We find the set equivalent martingale measures, and we hedge by minimizing the variance using Malliavin calculus.

Citations

• The Pricing of Options and Corporate Liabilities
• Empirical Performance of Alternative Option Pricing Models

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