The Eigenfunction Expansion Method in Multi-Factor Quadratic Term Structure Models

48 Pages Posted: 10 Jan 2006

See all articles by Nina Boyarchenko

Nina Boyarchenko

Federal Reserve Bank of New York

Sergei Levendorskii

Calico Science Consulting

Date Written: January 9, 2006

Abstract

We propose the eigenfunction expansion method for pricing options in linear-quadratic terms structure models. The eigenvalues, eigenfunctions and adjoint functions are calculated using elements of the representation theory of Lie algebras not only in the self-adjoint case but in non-selfadjoint case as well; the eigenfunctions and adjoint functions are expressed in terms of the Hermite polynomials. We demonstrate that the method is efficient for pricing caps, floors and swaptions, if time to maturity is 1 year or more. We also consider the subordination of the same class of models, and show that in the framework of the eigenfunction expansion approach, the subordinated models are (almost) as simple as pure Gaussian models. We study the dependence of option prices on the type of non-Gaussian innovations, and suggest parameters' fitting procedures based on the properties of the asymptotic expansions.

Keywords: Derivative pricing, swaptions, caps and floors, multi-factor exactly solvable models, eigenfunction expansion, continuous algebraic Riccati equations, Lyapunov equations, representation theory of Lie algebras, Hermite polynomials

JEL Classification: C60, C69

Suggested Citation

Boyarchenko, Nina and Levendorskii, Sergei Z., The Eigenfunction Expansion Method in Multi-Factor Quadratic Term Structure Models (January 9, 2006). Available at SSRN: https://ssrn.com/abstract=874839 or http://dx.doi.org/10.2139/ssrn.874839

Nina Boyarchenko

Federal Reserve Bank of New York ( email )

33 Liberty Street
New York, NY 10045
United States
212-720-7339 (Phone)
212-720-1582 (Fax)

Sergei Z. Levendorskii (Contact Author)

Calico Science Consulting ( email )

Austin, TX
United States

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