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The Jacobi Stochastic Volatility Model

Damien Ackerer, Damir Filipovi\'c and Sergio Pulido

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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.

New Economics Papers: this item is included in nep-ets and nep-rmg
Date: 2016-05, Revised 2018-03
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Published in Finance and Stochastics, Volume 22, Issue 3, Pages 667-700, 2018

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