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Journal Articles Finance and Stochastics Year : 2018

The Jacobi Stochastic Volatility Model

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.
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Dates and versions

hal-01338330 , version 1 (28-06-2016)
hal-01338330 , version 2 (18-07-2017)
hal-01338330 , version 3 (01-07-2018)
hal-01338330 , version 4 (08-08-2019)

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Cite

Damir Filipovic, Damien Ackerer, Sergio Pulido. The Jacobi Stochastic Volatility Model. Finance and Stochastics, 2018, 22 (3), pp.667-700. ⟨10.1007/s00780-018-0364-8⟩. ⟨hal-01338330v4⟩
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