Eigenfunction Expansion Method in Multi-Factor Models
52 Pages Posted: 1 Dec 2004
Date Written: November 30, 2004
Abstract
We show that three classes of multi-factor gaussian mean-reverting models: for the dynamics of the (log-)price of a stock, ATSM of the Ornstein-Uhlenbeck type, and QTSM are equivalent, when contingent claims with deterministic life-spans are considered. We provide the reduction of these models to two basic types of QTSMs, which are explicitly solved by the eigenfunction expansion technique. The reduction uses solutions to continuous algebraic Riccati equations and Lyapunov equations. The eigenvalues, eigenfunctions and adjoint functions are calculated by using elements of the representation theory of Lie algebras; the eigenfunctions and adjoint functions are expressed in terms of the Hermite polynomials. We also consider the same classes of models in random time, and show that in the framework of the eigenfunction expansion approach, the models in random time are (almost) as simple as pure gaussian models. We suggest parameters' fitting procedures based on the properties of the asymptotic expansions.
Keywords: Derivative pricing, multi-factor exactly solvable models, eigenfunction expansion, continuous algebraic Riccati equations, Lyapunov equations, representation theory of Lie algebras, Hermite polynomials
JEL Classification: E43
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Calibration and Implementation of Convertible Bond Models
By Leif B. G. Andersen and Dan Buffum
-
Time Changed Markov Processes in Unified Credit-Equity Modeling
By Peter Carr, Vadim Linetsky, ...
-
Pricing Convertible Bonds with Interest Rate, Equity, Credit, and FX Risk