Unifying pricing formula for several stochastic volatility models with jumps

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F17%3A43930082" target="_blank" >RIV/49777513:23520/17:43930082 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1002/asmb.2248" target="_blank" >http://dx.doi.org/10.1002/asmb.2248</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/asmb.2248" target="_blank" >10.1002/asmb.2248</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Unifying pricing formula for several stochastic volatility models with jumps

Popis výsledku v původním jazyce

In this paper, we introduce a unifying approach to option pricing under continuous-time stochastic volatility models with jumps. For European style options, a new semi-closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro-differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log-normal and a log-uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yani and Hanson respectively. The comparison of existing and newly proposed option pricing formulas with respect to time-efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out-of-the money contracts.

Název v anglickém jazyce

Unifying pricing formula for several stochastic volatility models with jumps

Popis výsledku anglicky

In this paper, we introduce a unifying approach to option pricing under continuous-time stochastic volatility models with jumps. For European style options, a new semi-closed pricing formula is derived using the generalized complex Fourier transform of the corresponding partial integro-differential equation. This approach is successfully applied to models with different volatility diffusion and jump processes. We also discuss how to price options with different payoff functions in a similar way. In particular, we focus on a log-normal and a log-uniform jump diffusion stochastic volatility model, originally introduced by Bates and Yani and Hanson respectively. The comparison of existing and newly proposed option pricing formulas with respect to time-efficiency and precision is discussed. We also derive a representation of an option price under a new approximative fractional jump diffusion model that differs from the aforementioned models, especially for the out-of-the money contracts.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50206 - Finance

Projekt

<a href="/cs/project/GA14-11559S" target="_blank" >GA14-11559S: Analýza frakcionálních modelů stochastické volatility a jejich implementace v gridu</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Applied Stochastic Models in Business and Industry

ISSN

1526-4025

e-ISSN

—

Svazek periodika

33

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

422-442

Kód UT WoS článku

000407654400010

EID výsledku v databázi Scopus

2-s2.0-85017385020