Artificial Boundary Method for European Pricing Option Problem

Abstract

This paper deals with the valuation of European call options under the Heston stochastic volatility model. An asymptotic solution of the European pricing option problem in powers of the volatility of variance is derived. An artificial boundary method for solving the problem on a truncated domain is considered and artificial boundary conditions are constructed. Numerical simulations show that these conditions allow to find more accurate numerical solutions than for the widely-used Heston boundary condition.