DG Method for Pricing European Options under Merton Jump-Diffusion Model

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F19%3A00007427" target="_blank" >RIV/46747885:24510/19:00007427 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27510/19:10242953

Výsledek na webu

<a href="https://articles.math.cas.cz/10.21136/AM.2019.0305-18" target="_blank" >https://articles.math.cas.cz/10.21136/AM.2019.0305-18</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.21136/AM.2019.0305-18" target="_blank" >10.21136/AM.2019.0305-18</a>

Jazyk výsledku

angličtina

Název v původním jazyce

DG Method for Pricing European Options under Merton Jump-Diffusion Model

Popis výsledku v původním jazyce

Under real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of analytical formulae. Obviously, any numerical technique should be tested for the cases when the analytical solution is well known. The paper is devoted to the discontinuous Galerkin method applied to European option pricing under the Merton jump-diffusion model, when the evolution of the asset prices is driven by a Lévy process with finite activity. The valuation of options under such a model with lognormally distributed jumps requires solving a parabolic partial integro-differential equation which involves both the integrals and the derivatives of the unknown pricing function. The integral term related to jumps leads to new theoretical and numerical issues regarding the solving of the pricing equation in comparison with the standard approach for the Black-Scholes equation. Here we adopt the idea of the relatively modern technique that the integral terms in Merton-type models can be viewed as solutions of proper differential equations, which can be accurately solved in a simple way. For practical purposes of numerical pricing of options in such models we propose a two-stage implicit-explicit scheme arising from the discontinuous piecewise polynomial approximation, i.e., the discontinuous Galerkin method. This solution procedure is accompanied with theoretical results and discussed within the numerical results on reference benchmarks.

Název v anglickém jazyce

DG Method for Pricing European Options under Merton Jump-Diffusion Model

Popis výsledku anglicky

Under real market conditions, there exist many cases when it is inevitable to adopt numerical approximations of option prices due to non-existence of analytical formulae. Obviously, any numerical technique should be tested for the cases when the analytical solution is well known. The paper is devoted to the discontinuous Galerkin method applied to European option pricing under the Merton jump-diffusion model, when the evolution of the asset prices is driven by a Lévy process with finite activity. The valuation of options under such a model with lognormally distributed jumps requires solving a parabolic partial integro-differential equation which involves both the integrals and the derivatives of the unknown pricing function. The integral term related to jumps leads to new theoretical and numerical issues regarding the solving of the pricing equation in comparison with the standard approach for the Black-Scholes equation. Here we adopt the idea of the relatively modern technique that the integral terms in Merton-type models can be viewed as solutions of proper differential equations, which can be accurately solved in a simple way. For practical purposes of numerical pricing of options in such models we propose a two-stage implicit-explicit scheme arising from the discontinuous piecewise polynomial approximation, i.e., the discontinuous Galerkin method. This solution procedure is accompanied with theoretical results and discussed within the numerical results on reference benchmarks.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA16-09541S" target="_blank" >GA16-09541S: Robustní numerická schémata pro oceňování vybraných opcí za různých tržních podmínek</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Applications of Mathematics

ISSN

0862-7940

e-ISSN

—

Svazek periodika

64

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

30

Strana od-do

501-530

Kód UT WoS článku

000491496200002

EID výsledku v databázi Scopus

2-s2.0-85073620538