The Jacobi Stochastic Volatility Model
Damir Filipovic (damir.filipovic@epfl.ch),
Damien Ackerer (damien.ackerer@epfl.ch) and
Sergio Pulido (sergio.pulidonino@ensiie.fr)
Additional contact information
Damir Filipovic: EPFL - Ecole Polytechnique Fédérale de Lausanne, Swiss Finance Institute [Lausanne] - EPFL - Ecole Polytechnique Fédérale de Lausanne
Damien Ackerer: EPFL - Ecole Polytechnique Fédérale de Lausanne, Swiss Finance Institute [Lausanne] - EPFL - Ecole Polytechnique Fédérale de Lausanne
Sergio Pulido: LaMME - Laboratoire de Mathématiques et Modélisation d'Evry - INRA - Institut National de la Recherche Agronomique - ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise - UEVE - Université d'Évry-Val-d'Essonne - CNRS - Centre National de la Recherche Scientifique, ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
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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 (search for similar items in EconPapers)
Date: 2018-07-01
Note: View the original document on HAL open archive server: https://hal.science/hal-01338330v4
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Citations: View citations in EconPapers (20)
Published in Finance and Stochastics, 2018, 22 (3), pp.667-700. ⟨10.1007/s00780-018-0364-8⟩
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01338330
DOI: 10.1007/s00780-018-0364-8
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