THE EIGENFUNCTION EXPANSION METHOD IN MULTI-FACTOR QUADRATIC TERM STRUCTURE MODELS
Source: Mathematical Finance, Volume 17, Number 4, October 2007 , pp. 503-539(37)
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.
Keywords: Hermite polynomials; Lyapunov equations; caps and floors; continuous algebraic Riccati equations; derivative pricing; eigenfunction expansion; multi-factor exactly solvable models; representation theory of Lie algebras; swaptions
Document Type: Research Article
Publication date: October 2007