Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method

Abstract

In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one- and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.

Keywords

• super-fast computation
• equity-linked securities
• black–scholes equations
• finite difference method