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Titolo:
Interest rates and information geometry
Autore:
Brody, DC; Hughston, LP;
Indirizzi:
Univ London Imperial Coll Sci Technol & Med, Blackett Lab, London SW7 2BZ,England Univ London Imperial Coll Sci Technol & Med London England SW7 2BZ gland Univ Cambridge, Ctr Math Sci, Cambridge CB3 0WA, England Univ Cambridge Cambridge England CB3 0WA Sci, Cambridge CB3 0WA, England Univ London Kings Coll, Dept Math, London WC2R 2LS, England Univ London Kings Coll London England WC2R 2LS London WC2R 2LS, England
Titolo Testata:
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
fascicolo: 2010, volume: 457, anno: 2001,
pagine: 1343 - 1363
SICI:
1364-5021(20010608)457:2010<1343:IRAIG>2.0.ZU;2-D
Fonte:
ISI
Lingua:
ENG
Soggetto:
TERM STRUCTURE; CONTINGENT CLAIMS;
Keywords:
interest rate models; Heath-Jarrow-Morton framework; arbitrage-free term-structure movements; differential geometry and statistics;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
Physical, Chemical & Earth Sciences
Citazioni:
50
Recensione:
Indirizzi per estratti:
Indirizzo: Brody, DC Univ London Imperial Coll Sci Technol & Med, Blackett Lab, Prince Consort Rd, London SW7 2BZ, England Univ London Imperial Coll Sci Technol& Med Prince Consort Rd London England SW7 2BZ
Citazione:
D.C. Brody e L.P. Hughston, "Interest rates and information geometry", P ROY SOC A, 457(2010), 2001, pp. 1343-1363

Abstract

The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter spacehas a Riemannian structure induced by the embedding of the family into theHilbert space of square-integrable functions, and is characterized by the Fisher-Rao metric. In tile non-parametric case the relevant geometry is determined by tile spherical distance function of Bhattacharyya. In the context of term-structure modelling, we show that the derivative of the discount,function with respect to the time left until maturity gives rise to a probability density. This follows as a consequence of the positivity of interest rates. Therefore, by mapping the density functions associated with a given family of term structures to Hilbert space, the resulting metrical geometry can be used to analyse the relationship of yield curves to one another. We show that tile general arbitrage-free yield-curve dynamics can be represented as a process taking values in the convex space of smooth density functions on the positive real line. It follows that tile theory of interest rate dynamics can be represented by a cla,ss of processes in Hilbert space. We also derive the dynamics for tile central moments associated with the distribution determined by the yield curve.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 10/07/20 alle ore 19:12:06