Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme. (1st June 2017)

• Record Type: Journal Article
• Authors: Li, Wen; Wang, Song
• Is Part Of: Computers & mathematics with applications. Volume 73:issue 11(2017)
• Page Start: 2454
• Page End: 2469
• Publication Date: 2017-06-01
• Subjects: Hamilton–Jacobi–Bellman equation -- Financial option valuation -- Finite volume method -- Penalty method -- Convergence; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.03.024
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper we propose a combination of a penalty method and a finite volume scheme for a four-dimensional time-dependent Hamilton–Jacobi–Bellman (HJB) equation arising from pricing European options with proportional transaction costs and stochastic volatility. The HJB equation is first approximated by a nonlinear partial differential equation containing penalty terms. A finite volume method along with an upwind technique is then developed for the spatial discretization of the nonlinear penalty equation. We show that the coefficient matrix of the discretized system is an M -matrix. An iterative method is proposed for solving the nonlinear algebraic system and a convergence theory is established for the iterative method. Numerical experiments are performed using a non-trivial model pricing problem and the numerical results demonstrate the usefulness of the proposed method.