A Geometric View of Interest Rate Theory
AbstractThe purpose of this essay is to give an overview of some recent workconcerning structural properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a given forward rate model consistent with a given family of forward rate curves? 2. When can the inherently infinite dimensional forward rate process be realized by means of a finite dimensional state space model. We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multi- dimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framwork we give necessary and sufficient conditions for consistency, as well as for the existence of a finite dimensional realization, in terms of the forward rate volatilities.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 419.
Length: 39 pages
Date of creation: 20 Dec 2000
Date of revision: 21 Dec 2000
Publication status: Published in Option pricing, Interest Rates and Risk Management, Jouini, Elyes, Cvitanic, Jaksa, Musiela, Marek (eds.), 2001, chapter 7, pages 241-277, Cambridge University Press.
Note: To appear in "Handbook of Mathematical Finance". Cambridge University Press
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More information through EDIRC
interest rates; Markovian realizations; forward rates; invariant manifold;
Find related papers by JEL classification:
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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