The Jacobi Stochastic Volatility Model

34 Pages Posted: 21 May 2016 Last revised: 30 Oct 2018

See all articles by Damien Ackerer

Damien Ackerer

affiliation not provided to SSRN

Damir Filipović

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute

Sergio Pulido

Laboratoire de Mathématiques et Modélisation d'Évry (LaMME); Université d'Évry-Val-d'Essonne, ENSIIE, Université Paris-Saclay, UMR CNRS 8071

Date Written: February 20, 2018

Abstract

We introduce a novel stochastic volatility model where the squared volatility of the asset return follows a Jacobi process. It contains the Heston model as a limit case. We show that the joint density of any finite sequence of log returns admits a Gram-Charlier A expansion with closed-form coefficients. We derive closed-form series representations for option prices whose discounted payoffs are functions of the asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and can be applied to discretely monitored Asian options. In a numerical analysis we show that option prices can be accurately and efficiently approximated by truncating their series representations.

Keywords: Jacobi process, option pricing, polynomial model, stochastic volatility

JEL Classification: C32, G12, G13

Suggested Citation

Ackerer, Damien and Filipovic, Damir and Pulido, Sergio, The Jacobi Stochastic Volatility Model (February 20, 2018). Finance and Stochastics, Volume 22, Issue 3, Pages 667-700, 2018; Swiss Finance Institute Research Paper No. 16-35. Available at SSRN: https://ssrn.com/abstract=2782486 or http://dx.doi.org/10.2139/ssrn.2782486

Damien Ackerer

affiliation not provided to SSRN

Damir Filipovic (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Odyssea
Station 5
Lausanne, 1015
Switzerland

HOME PAGE: http://people.epfl.ch/damir.filipovic

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Sergio Pulido

Laboratoire de Mathématiques et Modélisation d'Évry (LaMME); Université d'Évry-Val-d'Essonne, ENSIIE, Université Paris-Saclay, UMR CNRS 8071 ( email )

IBGBI 23 Boulevard de France
Évry Cedex, 91037
France

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