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The Jacobi stochastic volatility model. (English) Zbl 1402.91746
Summary: 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.

91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
60H30 Applications of stochastic analysis (to PDEs, etc.)
Full Text: DOI
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