2018/04/23 by Kuldip Singh Patel, Patel, Kuldip Singh, Mani Mehra +1
Economics, Econometrics and Finance · Mathematics · #Stochastic processes and financial applications #Differential Equations and Numerical Methods #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.1804.09043
In this article, a compact finite difference method is proposed for pricing\nEuropean and American options under jump-diffusion models. Partial\nintegro-differential equation and linear complementary problem governing\nEuropean and American options respectively are discretized using Crank-Nicolson\nLeap-Frog scheme. In proposed compact finite difference method, the second\nderivative is approximated by the value of unknowns and their first derivative\napproximations which allow us to obtain a tri-diagonal system of linear\nequations for the fully discrete problem. Further, consistency and stability\nfor the fully discrete problem are also proved. Since jump-diffusion models do\nnot have smooth initial conditions, the smoothing operators are employed to\nensure fourth-order convergence rate. Numerical illustrations for pricing\nEuropean and American options under Merton jump-diffusion model are presented\nto validate the theoretical results.\n