DG framework for pricing European options under one-factor stochastic volatility models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F46747885%3A24510%2F18%3A00006299" target="_blank" >RIV/46747885:24510/18:00006299 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61989100:27510/18:10240129

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cam.2018.05.064" target="_blank" >http://dx.doi.org/10.1016/j.cam.2018.05.064</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cam.2018.05.064" target="_blank" >10.1016/j.cam.2018.05.064</a>

Jazyk výsledku

angličtina

Název v původním jazyce

DG framework for pricing European options under one-factor stochastic volatility models

Popis výsledku v původním jazyce

The modern theory of option pricing is based on models introduced almost 50 years ago. These models, however, are not able to capture real market behaviour sufficiently well. One line of extensions consists of introducing an additional variable into the model, the so-called stochastic volatility. Since such models lead to the (semi) closed-form solution only rarely, some form of a numerical approximation can be essential. In this paper we study a general one-factor stochastic volatility model for the pricing of European options. A standard mathematical approach to this problem leads to a degenerate partial differential equation completed by boundary and terminal conditions. We formulate this problem in a variational sense and prove the existence and the uniqueness of a weak solution. Further, a robust numerical procedure based on the discontinuous Galerkin approach is proposed to improve the numerical valuation process. The performance of the procedure is accompanied with theoretical results and documented using reference experiments with the emphasis on investigation of the behaviour of option values with respect to the different mesh sizes as well as polynomial orders of approximation.

Název v anglickém jazyce

DG framework for pricing European options under one-factor stochastic volatility models

Popis výsledku anglicky

The modern theory of option pricing is based on models introduced almost 50 years ago. These models, however, are not able to capture real market behaviour sufficiently well. One line of extensions consists of introducing an additional variable into the model, the so-called stochastic volatility. Since such models lead to the (semi) closed-form solution only rarely, some form of a numerical approximation can be essential. In this paper we study a general one-factor stochastic volatility model for the pricing of European options. A standard mathematical approach to this problem leads to a degenerate partial differential equation completed by boundary and terminal conditions. We formulate this problem in a variational sense and prove the existence and the uniqueness of a weak solution. Further, a robust numerical procedure based on the discontinuous Galerkin approach is proposed to improve the numerical valuation process. The performance of the procedure is accompanied with theoretical results and documented using reference experiments with the emphasis on investigation of the behaviour of option values with respect to the different mesh sizes as well as polynomial orders of approximation.

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

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Computational and Applied Mathematics

ISSN

0377-0427

e-ISSN

—

Svazek periodika

344

Číslo periodika v rámci svazku

12

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

16

Strana od-do

585-600

Kód UT WoS článku

000440394900039

EID výsledku v databázi Scopus

2-s2.0-85048872281