Heath-Jarrow-Morton Type Models

Fred Espen Benth and Paul Krühner
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Fred Espen Benth: University of Oslo
Paul Krühner: Vienna University of Economics and Business

Chapter Chapter 6 in Stochastic Models for Prices Dynamics in Energy and Commodity Markets, 2023, pp 143-195 from Springer

Abstract: 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.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprfcp:978-3-031-40367-5_6

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DOI: 10.1007/978-3-031-40367-5_6

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