THE EIGENFUNCTION EXPANSION METHOD IN MULTI-FACTOR QUADRATIC TERM STRUCTURE MODELS

Authors


  • The authors are grateful to Vadim Linetsky for useful discussions and suggestions, and especially to the associate editor and two anonymous referees for a numerous valuable comments on the first two versions of the paper and recommendations. The usual disclaimer applies.

Address correspondence to Sergei Levendorskiǐ, The University of Texas at Austin, Department of Economics, 1 University Station C3100, Austin, TX, 78712-0301; e-mail: leven@eco.utexas.edu.

Abstract

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.

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