Pricing European options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme
MetadataShow full item record
© 2017 Elsevier Ltd 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.
Showing items related by title, author, creator and subject.
Wang, Song (2018)© 2017 Elsevier Inc. We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle ...
Penalty approach to a nonlinear obstacle problem governing American put option valuation under transaction costsLesmana, D.; Wang, Song (2015)We propose a penalty method for a finite-dimensional nonlinear complementarity problem (NCP) arising from the discretization of the infinite-dimensional free boundary/obstacle problem governing the valuation of American ...
An interior penalty method for a finite-dimensional linear complementarity problem in financial engineeringWang, Song; Zhang, K. (2018)© 2016, Springer-Verlag Berlin Heidelberg. In this work we study an interior penalty method for a finite-dimensional large-scale linear complementarity problem (LCP) arising often from the discretization of stochastic ...