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.
Highlights
The equity-linked security (ELS) is the financial derivative whose payoff relies on the performance of the underlying assets
The simple and explicit Euler scheme is used with the generated non-uniform grid, which demonstrates an optimal implementation of the algorithm for a super-fast three-asset ELS
We propose a systematic grid generation for fast finite difference method (FDM) for pricing a three-asset ELS as shown in
Summary
The equity-linked security (ELS) is the financial derivative whose payoff relies on the performance of the underlying assets. Priced European and American basket options with FDM They used a non-uniform sparse grid to reduce the computational time on high dimensions. In [17], Yoo et al compared the implicit method and explicit finite difference method for pricing ELS They used the modified BS equation using log-transformation and applied a non-systematically made non-uniform grid. To save the computational time when pricing ELS, the authors in [20] obtained a non-uniform grid by trial and error. They used an implicit scheme which requires solving a tridiagonal system of discrete equations. The simple and explicit Euler scheme is used with the generated non-uniform grid, which demonstrates an optimal implementation of the algorithm for a super-fast three-asset ELS option pricing.
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