Option Pricing under the Bates Model Using the Discontinuous Galerkin Method

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F22%3A00011947" target="_blank" >RIV/46747885:24510/22:00011947 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27510/22:10250544

Výsledek na webu

<a href="https://pubs.aip.org/aip/acp/article-abstract/2505/1/080007/2827703/Option-pricing-under-the-Bates-model-using-the" target="_blank" >https://pubs.aip.org/aip/acp/article-abstract/2505/1/080007/2827703/Option-pricing-under-the-Bates-model-using-the</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0100665" target="_blank" >10.1063/5.0100665</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Option Pricing under the Bates Model Using the Discontinuous Galerkin Method

Popis výsledku v původním jazyce

Stochastic volatility models with jumps generalize the classical Black-Scholes framework to capture more properly the real world features of option contracts. The extension is performed by incorporating jumps and a stochastic nature of volatility of asset returns into the dynamics of underlying asset prices. In this paper, we focus on pricing of European-style options under the Bates model that combines the Merton jump-diffusion model with a stochastic volatility proposed by Heston. As a result, the pricing function is governed by a partial-integro differential equation with two spatial variables, specifically, the price of the underlying asset and its variance. Moreover, the simultaneous presence of the non-local integral term arising from jumps increases the complexity of the problem. Therefore, to improve the numerical valuation we solve the corresponding governing equation by a discontinuous Galerkin approach with a semi-implicit time stepping scheme, where the differential part is treated implicitly while the integral one explicitly by the composite trapezoidal rule. Finally, the numerical results obtained are compared within the reference benchmark.

Název v anglickém jazyce

Option Pricing under the Bates Model Using the Discontinuous Galerkin Method

Popis výsledku anglicky

Stochastic volatility models with jumps generalize the classical Black-Scholes framework to capture more properly the real world features of option contracts. The extension is performed by incorporating jumps and a stochastic nature of volatility of asset returns into the dynamics of underlying asset prices. In this paper, we focus on pricing of European-style options under the Bates model that combines the Merton jump-diffusion model with a stochastic volatility proposed by Heston. As a result, the pricing function is governed by a partial-integro differential equation with two spatial variables, specifically, the price of the underlying asset and its variance. Moreover, the simultaneous presence of the non-local integral term arising from jumps increases the complexity of the problem. Therefore, to improve the numerical valuation we solve the corresponding governing equation by a discontinuous Galerkin approach with a semi-implicit time stepping scheme, where the differential part is treated implicitly while the integral one explicitly by the composite trapezoidal rule. Finally, the numerical results obtained are compared within the reference benchmark.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

AIP Conference Proceedings

ISBN

978-073544396-9

ISSN

0094-243X

e-ISSN

—

Počet stran výsledku

8

Strana od-do

—

Název nakladatele

American Institute of Physics Inc.

Místo vydání

Melville, NY

Místo konání akce

Sozopol, Bulgaria

Datum konání akce

1. 1. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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