A comparison study of explicit and implicit numerical methods for the equity-linked securities

Abstract

In this paper, we perform a comparison study of explicit and implicit numerical methods for the equity-linked securities (ELS). The option prices of the two-asset ELS are typically computed using an implicit finite difference method because an explicit finite difference scheme has a restriction for time steps. Nowadays, the three-asset ELS is getting popularity in the real world financial market. In practical applications of the finite difference methods in computational finance, we typically use relatively large space steps and small time steps. Therefore, we can use an accurate and efficient explicit finite difference method because the implementation is simple and the computation is fast. The computational results demonstrate that if we use a large space step, then the explicit scheme is better than the implicit one. On the other hand, if the space step size is small, then the implicit scheme is more efficient than the explicit one.