ON FINITE DIMENSIONAL REALIZATIONS FOR THE TERM STRUCTURE OF FUTURES PRICES

Tomas Bjork, Magnus Blix () and Camilla Landén ()
Additional contact information
Magnus Blix: Department of Finance, Stockholm School of Economics, Box 6501, SE-113 83 Stockholm, Sweden
Camilla Landén: Department of Mathematics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

International Journal of Theoretical and Applied Finance (IJTAF), 2006, vol. 09, issue 03, 281-314

Abstract: We consider HJM type models for the term structure of futures prices, where the volatility is allowed to be an arbitrary smooth functional of the present futures price curve. Using a Lie algebraic approach we investigate when the infinite dimensional futures price process can be realized by a finite dimensional Markovian state space model, and we give general necessary and sufficient conditions, in terms of the volatility structure, for the existence of a finite dimensional realization. We study a number of concrete applications including a recently developed model for gas futures. In particular we provide necessary and sufficient conditions for when the induced spot price is a Markov process. In particular we can prove that the only HJM type futures price models with spot price dependent volatility structures which generically possess a spot price realization are the affine ones. These models are thus the only generic spot price models from a futures price term structure point of view.

Keywords: HJM models; factor models; state space models; Markovian realizations (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (6)

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Working Paper: On finite dimensional realizations for the term structure of futures prices (2005)
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DOI: 10.1142/S0219024906003639

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