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- W14792380 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." @default.
- W14792380 created "2016-06-24" @default.
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- W14792380 date "2004-01-01" @default.
- W14792380 modified "2023-09-25" @default.
- W14792380 title "Eigenfunction Expansion Method in Multi-factor Models" @default.
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- W14792380 doi "https://doi.org/10.2139/ssrn.627642" @default.
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