Decomposition formula for rough Volterra stochastic volatility models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F21%3A43956997" target="_blank" >RIV/49777513:23520/21:43956997 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1142/S0219024921500084" target="_blank" >https://doi.org/10.1142/S0219024921500084</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0219024921500084" target="_blank" >10.1142/S0219024921500084</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Decomposition formula for rough Volterra stochastic volatility models

Popis výsledku v původním jazyce

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple non-linear financial derivatives as vanilla European options are typically priced by means of Monte-Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility -- a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models with rough fractional volatility and we derive an explicit semi-closed approximation formula. Numerical properties of the approximation for a popular model -- the rBergomi model -- are studied and we propose a hybrid calibration scheme which combines the approximation formula alongside MC simulations. This scheme can significantly speed up the calibration to financial markets as illustrated on a set of AAPL options.

Název v anglickém jazyce

Decomposition formula for rough Volterra stochastic volatility models

Popis výsledku anglicky

The research presented in this article provides an alternative option pricing approach for a class of rough fractional stochastic volatility models. These models are increasingly popular between academics and practitioners due to their surprising consistency with financial markets. However, they bring several challenges alongside. Most noticeably, even simple non-linear financial derivatives as vanilla European options are typically priced by means of Monte-Carlo (MC) simulations which are more computationally demanding than similar MC schemes for standard stochastic volatility models. In this paper, we provide a proof of the prediction law for general Gaussian Volterra processes. The prediction law is then utilized to obtain an adapted projection of the future squared volatility -- a cornerstone of the proposed pricing approximation. Firstly, a decomposition formula for European option prices under general Volterra volatility models is introduced. Then we focus on particular models with rough fractional volatility and we derive an explicit semi-closed approximation formula. Numerical properties of the approximation for a popular model -- the rBergomi model -- are studied and we propose a hybrid calibration scheme which combines the approximation formula alongside MC simulations. This scheme can significantly speed up the calibration to financial markets as illustrated on a set of AAPL options.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

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

2021

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

24

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

47

Strana od-do

2150008

Kód UT WoS článku

000649334300006

EID výsledku v databázi Scopus

2-s2.0-85104503511