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On Finite Dimensional Realizations of Forward Price Term Structure Models

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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, consists of 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 Björk 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.

Suggested Citation

  • Gaspar, Raquel M., 2004. "On Finite Dimensional Realizations of Forward Price Term Structure Models," SSE/EFI Working Paper Series in Economics and Finance 569, Stockholm School of Economics.
  • Handle: RePEc:hhs:hastef:0569
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    1. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    2. Björk, Tomas & Landen, Camilla, 2000. "On the construction of finite dimensional realizations for nonlinear forward rate models," SSE/EFI Working Paper Series in Economics and Finance 420, Stockholm School of Economics.
    3. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
    4. Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
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    Keywords

    Forward prices; term structures; state space models; Markovian realizations; HJM models;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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