Valuation of European call options for the Scott’s stochastic volatility model: An explicit finite difference scheme

Freddy H. Marín-Sánchez, Alejandro Pinilla Barrera, Cristhian Montoya Zambrano and Santiago Medina Hurtado

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 236, issue C, 411-425

Abstract: This paper addresses the construction of an explicit finite difference scheme for options valuation when the underlying asset is described by the stochastic volatility model proposed by Scott (1987). A numerical analysis of the scheme is conducted to ensure positivity, monotonicity, stability, consistency, and convergence conditions. Several numerical experiments are presented for the valuation of European call options, and the results obtained from the explicit finite difference scheme in 2D are compared with Monte Carlo simulations in order to show the feasibility of our results.

Keywords: Finite differences method; Numerical analysis; Black–Scholes equation; Scott model; Stochastic volatility (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:236:y:2025:i:c:p:411-425

DOI: 10.1016/j.matcom.2025.03.033

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