Adaptive and High-Order Methods for Valuing American Options

Journal of Computational Finance, Forthcoming

25 Pages Posted: 2 May 2010

See all articles by Christina Christara

Christina Christara

University of Toronto - Department of Computer Science

Duy-Minh Dang

University of Queensland - School of Mathematics and Physics

Date Written: April 29, 2010

Abstract

We develop space-time adaptive and high-order methods for valuing American options using a partial differential equation (PDE) approach. The linear complementarity problemarising due to the free boundary is handled by a penalty method. Both finite difference and finite element methods are considered for the space discretization of the PDE, while classical finite differences, such as Crank-Nicolson, are used for the time discretization. The high-order discretization in space is based on an optimal finite element collocation method, the main computational requirements of which are the solution of one tridiagonal linear system at each time step, while the resulting errors at the gridpoints and midpoints of the space partition are fourth-order. To control the space error, we use adaptive gridpoint distribution based on an error equidistribution principle. A time stepsize selector is used to further increase the efficiency of the methods. Numerical examples show that our methods converge fast and provide highly accurate options prices, Greeks, and early exercise boundaries

Keywords: Adaptive Mesh Selection, Error Equidistribution, Quadratic Splines, Collocation, Finite Differences, European Option, American Option, Penalty Method

JEL Classification: E40, E43, G12, G13, C61, C63

Suggested Citation

Christara, Christina and Dang, Duy-Minh, Adaptive and High-Order Methods for Valuing American Options (April 29, 2010). Journal of Computational Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1598948

Christina Christara

University of Toronto - Department of Computer Science ( email )

Department of Computer Science
University of Toronto
Toronto, Ontario M5S 3G4
Canada

Duy-Minh Dang (Contact Author)

University of Queensland - School of Mathematics and Physics ( email )

Priestly Building
St Lucia
Brisbane, Queesland 4067
Australia

HOME PAGE: http://people.smp.uq.edu.au/Duy-MinhDang/

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