Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F20%3A43930094" target="_blank" >RIV/49777513:23520/20:43930094 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1080/00207160.2019.1614174" target="_blank" >https://doi.org/10.1080/00207160.2019.1614174</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1080/00207160.2019.1614174" target="_blank" >10.1080/00207160.2019.1614174</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models

Popis výsledku v původním jazyce

In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of large number of integral evaluations with high precision and low computational time requirements. However, for some model parameters, many numerical quadrature algorithms fail to meet these requirements. We can observe an enormous increase in function evaluations, serious precision problems and a significant increase of computational time. In this paper we numerically analyse these problems and show that they are especially caused by inaccurately evaluated integrands. We propose a fast regime switching algorithm that tells if it is sufficient to evaluate the integrand in standard double arithmetic or if a higher precision arithmetic has to be used. We compare and recommend numerical quadratures for typical SV models and different parameter values, especially for problematic cases.

Název v anglickém jazyce

Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models

Popis výsledku anglicky

In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of large number of integral evaluations with high precision and low computational time requirements. However, for some model parameters, many numerical quadrature algorithms fail to meet these requirements. We can observe an enormous increase in function evaluations, serious precision problems and a significant increase of computational time. In this paper we numerically analyse these problems and show that they are especially caused by inaccurately evaluated integrands. We propose a fast regime switching algorithm that tells if it is sufficient to evaluate the integrand in standard double arithmetic or if a higher precision arithmetic has to be used. We compare and recommend numerical quadratures for typical SV models and different parameter values, especially for problematic cases.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

ISSN

0020-7160

e-ISSN

—

Svazek periodika

97

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

25

Strana od-do

1268-1292

Kód UT WoS článku

000470378200001

EID výsledku v databázi Scopus

2-s2.0-85065989340