The Jacobi Stochastic Volatility Model
34 Pages Posted: 21 May 2016 Last revised: 30 Oct 2018
Date Written: February 20, 2018
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
JEL Classification: C32, G12, G13
Suggested Citation: Suggested Citation