The Jacobi Stochastic Volatility Model

Damien Ackerer (1, 2) , Damir Filipovic (1, 2) , Sergio Pulido (3, 4)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 Swiss Finance Institute [Lausanne]
3 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
4 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise

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 find that the price approximations become accurate within short CPU time.

Keywords: Jacobi process; option pricing; polynomial model; stochastic volatility

Domains: Computational Finance [q-fin.CP]; Pricing of Securities [q-fin.PR]; Probability [math.PR]

Damien Ackerer, Damir Filipovic, Sergio Pulido. The Jacobi Stochastic Volatility Model. 2017. ⟨hal-01338330v2⟩