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

38 Pages Posted: 14 Sep 2007

See all articles by Nina Boyarchenko

Nina Boyarchenko

Federal Reserve Bank of New York

Sergei Levendorskii

Calico Science Consulting


We propose the eigenfunction expansion method for pricing options in quadratic term 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-self-adjoint case as well; the eigenfunctions and adjoint functions are expressed in terms of 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 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 Black implied volatilities and option prices on the type of non-Gaussian innovations.

Suggested Citation

Boyarchenko, Nina and Levendorskii, Sergei Z., The Eigenfunction Expansion Method in Multi-Factor Quadratic Term Structure Models. Mathematical Finance, Vol. 17, No. 4, pp. 503-539, October 2007. Available at SSRN: or

Nina Boyarchenko (Contact Author)

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

Calico Science Consulting ( email )

Austin, TX
United States

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