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SEPARABLE TERM STRUCTURES AND THE MAXIMAL DEGREE PROBLEM
Author(s) -
Filipović Damir
Publication year - 2002
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2002.tb00128.x
Subject(s) - term (time) , degree (music) , mathematics , quadratic equation , consistency (knowledge bases) , polynomial , diffusion , type (biology) , yield curve , quadratic function , separable space , degree of a polynomial , mathematical optimization , discrete mathematics , mathematical analysis , ecology , physics , geometry , quantum mechanics , biology , acoustics , thermodynamics
This paper discusses separablc term structure diffusion models in an arbitrage‐free environment. Using general consistency results we exploit the interplay between the diffusion coefficients and the functions determining the forward curve. We introduce the particular class of polynomial term structure models. We formulate the appropriate conditions under which the diffusion for a quadratic term structure model is necessarily an Ornstein‐Uhlenbeck type process. Finally, we explore the maximal degree problem and show that basically any consistent polynomial term structure model is of degree two or less.