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The Jacobi Stochastic Volatility Model

Damien Ackerer, Damir Filipović and Sergio Pulido
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Damien Ackerer: Ecole Polytechnique Fédérale de Lausanne; Ecole Polytechnique Fédérale de Lausanne - Swiss Finance Institute
Damir Filipović: Ecole Polytechnique Fédérale de Lausanne; 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, UMR CNRS 8071

No 16-35, Swiss Finance Institute Research Paper Series from Swiss Finance Institute

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 the joint distribution of any finite sequence of log returns admits a Gram-Charlier A expansion in closed-form. We use this to derive closed-form series representations for option prices whose payoff is a function of the underlying asset price trajectory at finitely many time points. This includes European call, put, and digital options, forward start options, and forward start options on the underlying return. We derive sharp analytical and numerical bounds on the series truncation errors. We illustrate the performance by numerical examples, which show that our approach offers a viable alternative to Fourier transform techniques.

Keywords: Jacobi process; option pricing; polynomial model; stochastic volatility (search for similar items in EconPapers)
JEL-codes: C32 G12 G13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ets
Date: 2016-05, Revised 2016-06
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