Decomposition formula for jump diffusion models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F18%3A43930096" target="_blank" >RIV/49777513:23520/18:43930096 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/S0219024918500528" target="_blank" >https://doi.org/10.1142/S0219024918500528</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219024918500528" target="_blank" >10.1142/S0219024918500528</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Decomposition formula for jump diffusion models

Popis výsledku v původním jazyce

In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston (1993) SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models - models utilizing a variance process postulated by Heston (1993). In particular, we inspect in detail the approximation formula for the Bates (1996) model with log-normal jump sizes and we provide a numerical comparison with the industry standard - Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behaviour under a specific SVJ model.

Název v anglickém jazyce

Decomposition formula for jump diffusion models

Popis výsledku anglicky

In this paper we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alos (2012) for Heston (1993) SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models - models utilizing a variance process postulated by Heston (1993). In particular, we inspect in detail the approximation formula for the Bates (1996) model with log-normal jump sizes and we provide a numerical comparison with the industry standard - Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behaviour under a specific SVJ model.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA18-16680S" target="_blank" >GA18-16680S: Rough modely frakcionální stochastické volatility</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

International Journal of Theoretical and Applied Finance

ISSN

0219-0249

e-ISSN

—

Svazek periodika

21

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

36

Strana od-do

1850052-1-1850052-36

Kód UT WoS článku

000455592700004

EID výsledku v databázi Scopus

2-s2.0-85056101528