On the Geometry of Interest Rate Models

Tomas Bjork

No 545, SSE/EFI Working Paper Series in Economics and Finance from Stockholm School of Economics

Abstract: In this paper, which is a substantial extension of the earlier essay Björk (2001), we give an overview of some recent work on the geometric 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 Markovian finite dimensional state space model.

We consider interest rate models of Heath-Jarrow-Morton type, where the forward rates are driven by a multidimensional Wiener process, and where he volatility is allowed to be an arbitrary smooth functional of the present forward rate curve. Within this framework 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. We also study stochastic volatility HJM models, and we provide a systematic method for the construction of concrete realizations.

Keywords: Forward rate curves; interest rate models; factor models; state space models; Markovian realizations (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Pages: 87 pages
Date: 2003-11-24
New Economics Papers: this item is included in nep-cba, nep-fin, nep-mon and nep-rmg
Note: To apppear in "Springer Lecture Notes in Mathematics"
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:hhs:hastef:0545

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