This monograph presents a theory for random field models in time and space, viewed as stochastic processes with values in a Hilbert space, to model the stochastic dynamics of forward and futures prices in energy, power, and commodity markets.
In this book, the well-known Heath–Jarrow–Morton approach from interest rate theory is adopted and extended into an infinite-dimensional framework, allowing for flexible modeling of price stochasticity across time and along the term structure curve. Various models are introduced based on stochastic partial differential equations with infinite-dimensional Lévy processes as noise drivers, emphasizing random fields described by low-dimensional parametric covariance functions instead of classical high-dimensional factor models. The Filipović space, a separable Hilbert space of Sobolev type, is found to be a convenient state space for the dynamics of forward and futures term structures. The monograph provides a classification of important operators in this space, covering covariance operators and the stochastic modeling of volatility term structures, including the Samuelson effect. Fourier methods are employed to price many derivatives of interest in energy, power, and commodity markets, and sensitivity ‘delta’ expressions can be derived. Additionally, the monograph covers forward curve smoothing, the connection between forwards with fixed delivery and delivery period, as well as the classical theory of forward and futures pricing.
This monograph will appeal to researchers and graduate students interested in mathematical finance and stochastic analysis applied in the challenging markets of energy, power, and commodities. Practitioners seeking sophisticated yet flexible and analytically tractable risk models will also find it valuable.
Mục lục
1 Introduction.- Part I: Mathematical Tools.- 2 Lévy processes on Hilbert spaces.- 3 The Filipović space and operators.- 4 Stochastic integration and partial differential equations.- Part II: Modelling the Forward Price Dynamics and Derivatives Pricing.- 5 Spot models and forward pricing.- 6 Heath–Jarrow–Morton type models.- 7 Pricing of commodity and energy options.- Appendix A: Collection of some fundamental properties of the Filipović space.
Giới thiệu về tác giả
Fred Espen Benth is a professor of mathematics at the University of Oslo. His research interests are at the cross-roads of stochastic analysis, mathematical finance and energy markets. He has co-authored three monographs on topics ranging from ambit stochastics to energy and weather markets, as well as co-edited two volumes with a focus on energy markets. Recently, his research has been directed to renewable energy systems and machine learning. Fred Espen Benth is an elected member of the Norwegian Academy of Science and Letters and a former co-leader of the Center of Advanced Studies (CAS) in Oslo.
Paul Krühner (Eisenberg) is an assistant professor at the Institute of Statistics and Mathematics of the Vienna University of Economics and Business (WU). His research interests are in the field of stochastic analysis, mathematical finance and energy markets and include topics like Levy processes, occupation bounds and dynamic parameter models. Paul Eisenberg has also made contributions to insurance mathematics. Recently, his research focus has been directed to finite dimensional term structure models.
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