Numerical Pricing of European Options Under the Double Exponential Jump-Diffusion Model With Stochastic Volatility

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F23%3A00011945" target="_blank" >RIV/46747885:24510/23:00011945 - isvavai.cz</a>

Výsledek na webu

<a href="https://pubs.aip.org/aip/acp/article-abstract/2849/1/090001/2909004/Numerical-pricing-of-European-options-under-the" target="_blank" >https://pubs.aip.org/aip/acp/article-abstract/2849/1/090001/2909004/Numerical-pricing-of-European-options-under-the</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1063/5.0163421" target="_blank" >10.1063/5.0163421</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical Pricing of European Options Under the Double Exponential Jump-Diffusion Model With Stochastic Volatility

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 model that combines the Heston stochastic volatility model with the Kou-type double exponential jumps in the underlying prices. As a result, the pricing function is governed by a partial-integro differential equation having the price of the underlying asset and its variance as spatial variables. Moreover, a presence of the non-local operator arising from jumps increases the complexity of the problem. Therefore, to improve the numerical pricing process we solve the relevant pricing equation by a discontinuous Galerkin approach with a semi-implicit time stepping scheme, where the differential operator is treated implicitly while the integral one explicitly by a composite trapezoidal rule. Finally, the numerical results demonstrate the capability of the numerical approach presented within the simple experiments.

Název v anglickém jazyce

Numerical Pricing of European Options Under the Double Exponential Jump-Diffusion Model With Stochastic Volatility

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 model that combines the Heston stochastic volatility model with the Kou-type double exponential jumps in the underlying prices. As a result, the pricing function is governed by a partial-integro differential equation having the price of the underlying asset and its variance as spatial variables. Moreover, a presence of the non-local operator arising from jumps increases the complexity of the problem. Therefore, to improve the numerical pricing process we solve the relevant pricing equation by a discontinuous Galerkin approach with a semi-implicit time stepping scheme, where the differential operator is treated implicitly while the integral one explicitly by a composite trapezoidal rule. Finally, the numerical results demonstrate the capability of the numerical approach presented within the simple experiments.

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

2023

Kód důvěrnosti údajů

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

Název statě ve sborníku

AIP Conference Proceedings

ISBN

—

ISSN

0094-243X

e-ISSN

—

Počet stran výsledku

4

Strana od-do

—

Název nakladatele

American Institute of Physics Inc.

Místo vydání

Melville, NY

Místo konání akce

Rhodes

Datum konání akce

1. 1. 2021

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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