An efficient numerical method for American options and their Greeks under the two-asset Kou jump-diffusion model

TL;DR

This paper introduces an efficient numerical method for pricing American options and calculating their Greeks under a two-asset Kou jump-diffusion model, utilizing advanced discretization and iteration techniques.

Contribution

It extends the fast algorithm for single-asset Kou models to two assets and combines it with second-order DIRK methods for improved accuracy.

Findings

Achieves second-order convergence for option value and Greeks

Demonstrates efficiency through numerical experiments

Provides a practical approach for two-asset American options

Abstract

In this paper we consider the numerical solution of the two-dimensional time-dependent partial integro-differential complementarity problem (PIDCP) that holds for the value of American-style options under the two-asset Kou jump-diffusion model. Following the method of lines (MOL), we derive an efficient numerical method for the pertinent PIDCP. Here, for the discretization of the nonlocal double integral term, an extension is employed of the fast algorithm by Toivanen (2008) in the case of the one-asset Kou jump-diffusion model. For the temporal discretization, we study a useful family of second-order diagonally implicit Runge-Kutta (DIRK) methods. Their adaptation to the semidiscrete two-dimensional Kou PIDCP is obtained by means of an effective iteration introduced by d'Halluin, Forsyth & Labahn (2004) and d'Halluin, Forsyth & Vetzal (2005). Ample numerical experiments are presented showing that the proposed numerical method achieves a favourable, second-order convergence behaviour to the American two-asset option value as well as to its Greeks Delta and Gamma.