Finite Dimensional Markovian Realizations for Forward Price Term Structure Models
STOCHASTIC FINANCE, M. Grossinho, A. Shyriaev, M. Esquvel, P. Oliveira, eds. , Chapter 10, pp. 265-320, Springer Verlag Publisher, 2006
51 Pages Posted: 17 Jul 2006 Last revised: 7 Jul 2008
Date Written: 2006
Abstract
In this paper we study a fairly general Wiener driven model for the term structure of forward prices.
The model, under a fixed martingale measure, Q, is described by using two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest rates, driven by a multidimensional Wiener process W. The second system is an infinite SDE for the term structure of forward prices on some specified underlying asset driven by the same W. We are primarily interested in the forward prices. However, since for any fixed maturity T, the forward price process is a martingale under the T-forward neutral measure, the zero coupon bond volatilities will enter into the drift part of the SDE for these forward prices. The interest rate system is, thus, needed as input into the forward price system.
Given this setup we use the Lie algebra methodology of Bjork et al. to investigate under what conditions on the volatility structure of the forward prices and/or interest rates, the inherently (doubly) infinite dimensional SDE for forward prices can be realized by a finite dimensional Markovian state space model.
Keywords: forward prices, term structures, state space models, Markovian realizations, HJM models
JEL Classification: E43, G13
Suggested Citation: Suggested Citation
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