A hybrid stochastic volatility model in a Lévy market

Youssef El-Khatib; Stephane Goutte; Zororo S. Makumbe; Josep Vives

doi:10.1016/j.iref.2023.01.005

A hybrid stochastic volatility model in a Lévy market

Youssef El-Khatib, Stephane Goutte, Zororo S. Makumbe, Josep Vives

Department of Mathematical Sciences

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

Abstract

This paper deals with the problem of pricing and hedging financial options in a hybrid stochastic volatility model with jumps and a comparative study of its stylized facts. Under these settings, the market is incomplete, which leads to the existence of infinitely many risk-neutral measures. In order to price an option, a set of risk-neutral measures is determined. Moreover, the PIDE of an option price is derived using the Itô formula. Furthermore, Malliavin–Skorohod Calculus is utilized to hedge options and compute price sensitivities. The obtained results generalize the existing pricing and hedging formulas for the Heston as well as for the CEV stochastic volatility models.

Original language	English
Pages (from-to)	220-235
Number of pages	16
Journal	International Review of Economics and Finance
Volume	85
DOIs	https://doi.org/10.1016/j.iref.2023.01.005
Publication status	Published - May 2023

Keywords

European options
Lévy processes
Monte Carlo method
Numerical simulations
Stochastic volatility Black and Scholes Formula

ASJC Scopus subject areas

Finance
Economics and Econometrics

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10.1016/j.iref.2023.01.005

Cite this

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title = "A hybrid stochastic volatility model in a L{\'e}vy market",

abstract = "This paper deals with the problem of pricing and hedging financial options in a hybrid stochastic volatility model with jumps and a comparative study of its stylized facts. Under these settings, the market is incomplete, which leads to the existence of infinitely many risk-neutral measures. In order to price an option, a set of risk-neutral measures is determined. Moreover, the PIDE of an option price is derived using the It{\^o} formula. Furthermore, Malliavin–Skorohod Calculus is utilized to hedge options and compute price sensitivities. The obtained results generalize the existing pricing and hedging formulas for the Heston as well as for the CEV stochastic volatility models.",

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author = "Youssef El-Khatib and Stephane Goutte and Makumbe, {Zororo S.} and Josep Vives",

note = "Funding Information: This work was supported by the United Arab Emirates University Research Office via the UAEU [UPAR Grant No. 31S369 ] and partially supported by Spanish grant PID2020-118339GB-100 (2021–2024) . Publisher Copyright: {\textcopyright} 2023 Elsevier Inc.",

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AU - Goutte, Stephane

AU - Makumbe, Zororo S.

AU - Vives, Josep

N1 - Funding Information: This work was supported by the United Arab Emirates University Research Office via the UAEU [UPAR Grant No. 31S369 ] and partially supported by Spanish grant PID2020-118339GB-100 (2021–2024) . Publisher Copyright: © 2023 Elsevier Inc.

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N2 - This paper deals with the problem of pricing and hedging financial options in a hybrid stochastic volatility model with jumps and a comparative study of its stylized facts. Under these settings, the market is incomplete, which leads to the existence of infinitely many risk-neutral measures. In order to price an option, a set of risk-neutral measures is determined. Moreover, the PIDE of an option price is derived using the Itô formula. Furthermore, Malliavin–Skorohod Calculus is utilized to hedge options and compute price sensitivities. The obtained results generalize the existing pricing and hedging formulas for the Heston as well as for the CEV stochastic volatility models.

AB - This paper deals with the problem of pricing and hedging financial options in a hybrid stochastic volatility model with jumps and a comparative study of its stylized facts. Under these settings, the market is incomplete, which leads to the existence of infinitely many risk-neutral measures. In order to price an option, a set of risk-neutral measures is determined. Moreover, the PIDE of an option price is derived using the Itô formula. Furthermore, Malliavin–Skorohod Calculus is utilized to hedge options and compute price sensitivities. The obtained results generalize the existing pricing and hedging formulas for the Heston as well as for the CEV stochastic volatility models.

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KW - Lévy processes

KW - Monte Carlo method

KW - Numerical simulations

KW - Stochastic volatility Black and Scholes Formula

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A hybrid stochastic volatility model in a Lévy market

Abstract

Keywords

ASJC Scopus subject areas

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