Second-order lattice Boltzmann methods for PDEs of Asian option pricing with regime switching

This paper establishes lattice Boltzmann models with five amending functions for solving system of partial differential equations (PDEs) arising in Asian options pricing with regime switching. With the Chapman–Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and then the lattice Boltzmann method (LBM) is proposed. In the LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants in the traditional LBMs. The LBM has second-order convergence rate in space and first-order convergence rate in time. The stability, convergence rates and computational cost of LBMs are studied and verified by numerical examples.