Option pricing and hedging under a stochastic volatility Lévy process model

Young Shin Kim; Frank J. Fabozzi; Zuodong Lin; Svetlozar T. Rachev

doi:10.1007/s11147-011-9070-9

Option pricing and hedging under a stochastic volatility Lévy process model

Young Shin Kim, Frank J. Fabozzi, Zuodong Lin, Svetlozar T. Rachev

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

In this paper, we discuss a stochastic volatility model with a Lévy driving process and then apply the model to option pricing and hedging. The stochastic volatility in our model is defined by the continuous Markov chain. The risk-neutral measure is obtained by applying the Esscher transform. The option price using this model is computed by the Fourier transform method. We obtain the closed-form solution for the hedge ratio by applying locally risk-minimizing hedging.

Original language	English
Pages (from-to)	81-97
Number of pages	17
Journal	Review of Derivatives Research
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s11147-011-9070-9
State	Published - Apr 2012

Keywords

Continuous Markov chain
Esscher transform
Hedging
Lévy process
Option pricing
Regime-switching model
Stochastic volatility

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10.1007/s11147-011-9070-9

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abstract = "In this paper, we discuss a stochastic volatility model with a L{\'e}vy driving process and then apply the model to option pricing and hedging. The stochastic volatility in our model is defined by the continuous Markov chain. The risk-neutral measure is obtained by applying the Esscher transform. The option price using this model is computed by the Fourier transform method. We obtain the closed-form solution for the hedge ratio by applying locally risk-minimizing hedging.",

keywords = "Continuous Markov chain, Esscher transform, Hedging, L{\'e}vy process, Option pricing, Regime-switching model, Stochastic volatility",

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AB - In this paper, we discuss a stochastic volatility model with a Lévy driving process and then apply the model to option pricing and hedging. The stochastic volatility in our model is defined by the continuous Markov chain. The risk-neutral measure is obtained by applying the Esscher transform. The option price using this model is computed by the Fourier transform method. We obtain the closed-form solution for the hedge ratio by applying locally risk-minimizing hedging.

KW - Continuous Markov chain

KW - Esscher transform

KW - Hedging

KW - Lévy process

KW - Option pricing

KW - Regime-switching model

KW - Stochastic volatility

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Option pricing and hedging under a stochastic volatility Lévy process model

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