Numerical solution for option pricing with stochastic volatility model

Workshop and International Seminar on Science of Complex Natural Systems

Mariani, Andi^1 ; Nugrahani, Endar H.^1 ; Lesmana, Donny C.^1

Department of Mathematics, Bogor Agricultural University, Kampus IPB Dramaga, Jalan Meranti, Bogor

16680, Indonesia^1

关键词: Approximate solution;    Finite difference scheme;    Nonlinear partial differential equations;    Numerical experiments;    Order of convergence;    Stochastic Volatility Model;    Time-stepping schemes;    Viscosity solutions;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/31/1/012024/pdf
DOI  :  10.1088/1755-1315/31/1/012024

来源: IOP

【 摘 要 】

The option pricing equations derived from stochatic volatility models in finance are often cast in the form of nonlinear partial differential equations. To solve the equations, we used the upwind finite difference scheme for the spatial discretisation and a fully implicit time-stepping scheme. The result of this scheme is a matrix system in the form of an M-Matrix and we proof that the approximate solution converges to the viscosity solution to the equation by showing that the scheme is monotone, consistent and stable. Numerical experiments are implemented to show that the behavior and the order of convergence of upwind finite difference method.