Stabilized explicit Runge-Kutta methods for multi-asset American options

Authors:
J. Martín-Vaquero;A. Q. M. Khaliq;B. Kleefeld
Affiliations:
-;-;-
Venue:
Computers & Mathematics with Applications
Year:
2014

Citing 14
Cited 0

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Abstract

American derivatives have become very popular instruments in financial markets. However, they are more complicated to price than European options since at each time level we have to determine not only the option value but also whether or not it should be exercised. Several procedures have been proposed to dissolve these difficulties, but they usually involve the solution of nonlinear partial differential equations (PDEs). In the case of multi-dimensional problems, solving these equations is a very challenging task. In this paper we propose Stabilized Explicit Runge-Kutta (SERK) methods to solve this kind of problems. They can easily be applied to many different classes of problems with large dimensions and they have low memory demand. Since these methods are explicit, they do not require algebra routines to solve large nonlinear systems associated to ODEs (as, for example, LAPACK and BLAS packages or multigrid or iterative methods applied together with Newton-type algorithms) and are especially well-suited for the method of lines (MOL) discretizations of parabolic PDEs.