Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model

Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model...

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Main Author: Guohe Deng
Format: Article
Language:English
Published: Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/1960121
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author Guohe Deng
author_facet Guohe Deng
author_sort Guohe Deng
collection DOAJ
description Empirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.
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spelling doaj-art-f6d8cc6d6eba4b66990655e8f65e64bf2025-02-03T01:03:40ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/19601211960121Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion ModelGuohe Deng0College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, ChinaEmpirical evidence shows that single-factor stochastic volatility models are not flexible enough to account for the stochastic behavior of the skew, and certain financial assets may exhibit jumps in returns and volatility. This paper introduces a two-factor stochastic volatility jump-diffusion model in which two variance processes with jumps drive the underlying stock price and then considers the valuation on European style option. We derive a semianalytical formula for European vanilla option and develop a fast and accurate numerical algorithm for the computation of the option prices using the fast Fourier transform (FFT) technique. We compare the volatility smile and probability density of the proposed model with those of alternative models, including the normal jump diffusion model and single-factor stochastic volatility model with jumps, respectively. Finally, we provide some sensitivity analysis of the model parameters to the options and several calibration tests using option market data. Numerical examples show that the proposed model has more flexibility to capture the implied volatility term structure and is suitable for empirical work in practice.http://dx.doi.org/10.1155/2020/1960121
spellingShingle Guohe Deng
Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
Complexity
title Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
title_full Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
title_fullStr Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
title_full_unstemmed Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
title_short Option Pricing under Two-Factor Stochastic Volatility Jump-Diffusion Model
title_sort option pricing under two factor stochastic volatility jump diffusion model
url http://dx.doi.org/10.1155/2020/1960121
work_keys_str_mv AT guohedeng optionpricingundertwofactorstochasticvolatilityjumpdiffusionmodel