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

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 privce 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 concrefe 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: futures contract; term structure; Lie algebra; finite dimensional realisation

JEL-codes: G13

37 pages, October 20, 2005

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