New Splitting Scheme for Pricing American Options Under the Heston Model

In this paper, we present a new splitting scheme for pricing the American options under the Heston model. For this purpose, first the price of American put option is modeled, which its underlying asset value follows Heston’s stochastic volatility model , and then it is formulated as a linear complementarity problem (LCP) involving partial differential operator. By using new splitting scheme, the partial differential operator is decomposed into simpler operators in several fractional time steps. These operators are implicitly expressed in the implicit Adams–Moulton method. Then, the two-dimensional LCP is decomposed into three LCPs based on these operators. Each LCP is solved numerically in two steps. The numerical results obtained for the American option pricing problem based on the Heston model are compared with the reference results.