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Heath-Jarrow-Morton Type Models

Author

Listed:
  • Fred Espen Benth

    (University of Oslo)

  • Paul Krühner

    (Vienna University of Economics and Business)

Abstract

In this main chapter of the book, infinite-dimensional stochastic processes are defined for the forward dynamics using a Hilbert space as state space for the term structures. Arithmetic and geometric models are introduced, where the noise driver is a Wiener process or a Lévy process and the context is cross-commodity markets. Moreover, we also allow for a class of stochastic volatility models in the forward dynamics. Drift conditions are derived ensuring a risk-neutral dynamics, i.e., a no-arbitrage dynamics under a pricing measure. We furthermore study swap prices (forward with delivery period) and finite factor models in this HJM-framework. To include seasonality and modeling under the market probability require a study of measure change, where one may apply the Girsanov and Esscher transform in our context. To have available data and the initial forward curve, a smoothing approach based on a combination of parametric curves (i.e., the Nelson-Siegel model) the the interpolation technique kriging is proposed and applied in an empirical example.

Suggested Citation

Handle: RePEc:spr:sprfcp:978-3-031-40367-5_6
DOI: 10.1007/978-3-031-40367-5_6
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