Decomposition formula for rough Volterra stochastic volatility models

Result code in 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>

Result on the web

<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>

Result language

angličtina

Original language name

Decomposition formula for rough Volterra stochastic volatility models

Original language description

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.

Czech name

—

Czech description

—

Type

J_SC - Article in a specialist periodical, which is included in the SCOPUS database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA18-16680S" target="_blank" >GA18-16680S: Rough models of fractional stochastic volatility</a><br>

Continuities

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

Publication year

2021

Confidentiality

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

Name of the periodical

International Journal of Theoretical and Applied Finance

ISSN

0219-0249

e-ISSN

—

Volume of the periodical

24

Issue of the periodical within the volume

2

Country of publishing house

SG - SINGAPORE

Number of pages

47

Pages from-to

2150008

UT code for WoS article

000649334300006

EID of the result in the Scopus database

2-s2.0-85104503511