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The Jacobi stochastic volatility model

Damien Ackerer (), Damir Filipović () and Sergio Pulido ()
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Damien Ackerer: Swissquote Bank
Damir Filipović: EPFL and Swiss Finance Institute
Sergio Pulido: Université Paris-Saclay

Finance and Stochastics, 2018, vol. 22, issue 3, 667-700

Abstract: 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 study, 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; 91B25; 91B70; 91G20; 91G60 (search for similar items in EconPapers)
JEL-codes: C32 G12 G13 (search for similar items in EconPapers)
Date: 2018
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