Adaptive and high-order methods for valuing American options

Christara, Christina C. and Dang, Duy-Minh (2011) Adaptive and high-order methods for valuing American options. Journal of Computational Finance, 14 4: .

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Name Description MIMEType Size Downloads
Author Christara, Christina C.
Dang, Duy-Minh
Title Adaptive and high-order methods for valuing American options
Journal name Journal of Computational Finance   Check publisher's open access policy
ISSN 1460-1559
1755-2850
Publication date 2011
Year available 2011
Sub-type Article (original research)
Volume 14
Issue 4
Total pages 25
Place of publication Haymarket, London, United Kingdom
Publisher Incisive Media Ltd.
Collection year 2011
Language eng
Formatted abstract
We develop space-time adaptive and high-order methods for valuing American options using a partial differential equation (PDE) approach. The linear complementarity problem arising 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.
Keyword Finite element methods
Spine collocation
Parabolic problems
Convergence
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Wed, 17 Sep 2014, 16:16:16 EST by Kay Mackie on behalf of School of Mathematics & Physics