On the construction of finite dimensional realizations for nonlinear forward rate models

Tomas Bjork and Camilla Landen (camilla@math.kth.se)
Additional contact information
Camilla Landen: Department of Mathematics, Postal: Royal Institute of Technology, S-100 44 Stockholm, Sweden

No 420, SSE/EFI Working Paper Series in Economics and Finance from Stockholm School of Economics

Abstract: We consider interest rate models of Heath-Jarrow-Morton type where the forward rates are driven by a multidimensional Wiener process, and where the volatility structure is allowed to be a smooth functional of the present forward rate curve.

In a recent paper (to appear in "Mathematical Finance" ) Björk and Svensson give necessary and sufficient conditions for the existence of a finite dimensional Markovian state space realization (FDR) for such a forward rate model, and in the present paper we provide a general method for the actual construction of an FDR.

The method works as follows: From the results of Björk and Svensson we know that there exists an FDR if and only if a certain Lie algebra is finite dimensional. Given a set of generators for this Lie algebra we show how to construct an FDR by solving a finite number of ordinary differential equations in Hilbert space. We illustrate the method by constructing FDR:s for a number of concrete models. These FDR:s generalize previous results by allowing for a more general volatility structure. Furthermore, the dimension of the realizations obtained by using our method is typically smaller than that of the corresponding previously known realizations. We also show how to obtain realizations in terms of benchmarforward rates from the realizations obtained using our method, and finally we present a bond pricing formula for the realizations we have obtained.

Keywords: forward rate; HJM models; term structure; factor models; state space models; Markovian realizations (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2000-12-20
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (16)

Forthcoming in Finance and Stochastics.

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Related works:
Journal Article: On the construction of finite dimensional realizations for nonlinear forward rate models (2002)
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