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Characterizing Gaussian Models of the Term Structure of Interest Rates
Author(s) -
Kennedy D. P.
Publication year - 1997
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 - 10.1111/1467-9965.00026
Subject(s) - covariance , martingale (probability theory) , gaussian , mathematics , term (time) , markov chain , statistical physics , econometrics , markov process , gaussian random field , gaussian process , statistics , physics , quantum mechanics
Models of the term structure of interest rates are considered for which, under the martingale measure, instantaneous forward rates are Gaussian. The possible forms of the covariance structure are characterized under appropriate formulations of the Markov property. It is demonstrated that imposing Markovian assumptions limits severely the covariances that may be obtained and that the strongest such formulation together with stationarity implies that the whole forward rate surface is necessarily a Gaussian random field described by just three parameters.