Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 498: Finite dimensional Markovian realizations for stochastic volatility forward rate models

Tomas Björk (), Camilla Landén and Lars Svensson ()
Additional contact information
Tomas Björk: Dept. of Finance, Stockholm School of Economics, Postal: Stockholm School of Economics, P.O. Box 6501, SE-113 83 Stockholm, Sweden
Camilla Landén: Länsförsäkringar Liv, Postal: Länsförsäkringar Liv, SE-173 81 Stockholm, Sweden
Lars Svensson: Department of Mathematics, Royal Institute of Technology, Postal: Department of Mathematics, KTH, SE-100 44 Stockholm, Sweden

Abstract: We consider forward rate rate models of HJM type, as well as more general infinite dimensional SDEs, where the volatility/diffusion term is stochastic in the sense of being driven by a separate hidden Markov process. Within this framework we use the previously developed Hilbert space realization theory in order provide general necessary and sufficent conditions for the existence of a finite dimensional Markovian realizations for the stochastic volatility models. We illustrate the theory by analyzing a number of concrete examples.

Keywords: HJM models; stochastic volatility; factor models; forward rates; state space models; Markovian realizations; infinite dimensional SDEs

JEL-codes: E43; G13

47 pages, First version: April 29, 2002. Revised: May 7, 2002. Earlier revisions: May 6, 2002.

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