Hedging electricity swaptions using partial integro-differential equations

Hepperger, Peter

doi:10.1016/j.spa.2011.09.005

Cited by 13 publications

(10 citation statements)

References 22 publications

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“…We also state the Hilbert space-valued forward curve model there. For a more detailed analysis of the model, we refer to [9]. Section 3 is concerned with the quadratic hedging problem for a swaption.…”

Section: Outline Of the Articlementioning

confidence: 99%

“…We also give a compact overview of the function-valued stochastic process which we use to model the forward curve. This model has been discussed in detail in [9].…”

Section: A Hilbert Space-valued Model For Electricity Swapsmentioning

confidence: 99%

“…We start with a formal description of the portfolio of swaps and the hedging problem. It has been shown in [9] that every optimal strategy solves a linear equation system for each point in time. There are two numerical issues when solving these equations.…”

Section: Computing An Optimal Hedging Strategymentioning

confidence: 99%

“…Based on this model, we propose an algorithm to solve the quadratic hedging problem for European options. In [9], it has been shown that the mean-variance hedging strategy in this setting is obtained by solving linear equation systems. The parameters of these equations, however, depend on the solution of an infinite-dimensional partial integro-differential equation (PIDE) for the swaption price.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Hedging of Electricity Contracts Using Dimension Reduction

Hepperger

2012

Int. J. Theor. Appl. Finan.

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The basic contracts traded on energy exchanges involve fixed-rate payments for the delivery of electricity over a certain period of time. It has been shown that options on these electricity swaps can be priced efficiently using a Hilbert space-valued time-inhomogeneous jump-diffusion model for the forward curve. We consider the mean-variance hedging problem for European options under this model. The computation of hedging strategies leads to quadratic optimization problems whose parameters depend on the solution of an infinite-dimensional partial integro-differential equation. The main objective of this article is to find an efficient numerical algorithm for this task. Using proper orthogonal decomposition (a dimension reduction method), approximately optimal strategies are computed. We prove convergence of the corresponding hedging error to the minimal achievable error in the electricity market. Numerical experiments are performed to analyze the resulting hedging strategies.

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Section: Outline Of the Articlementioning

confidence: 99%

“…We also give a compact overview of the function-valued stochastic process which we use to model the forward curve. This model has been discussed in detail in [9].…”

Section: A Hilbert Space-valued Model For Electricity Swapsmentioning

confidence: 99%

Section: Computing An Optimal Hedging Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical Hedging of Electricity Contracts Using Dimension Reduction

Hepperger

2012

Int. J. Theor. Appl. Finan.

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“…Abergel [10] used a nonlinear PIDE in financial modelling. Hepperger [11] proposed a PIDE in the model of electricity swaptions. A PIDE governing biofluid flow in fractured biomaterials is proposed by Zadeh in [12].…”

Section: Introductionmentioning

confidence: 99%

Solving Partial Integro-Differential Equations Using Laplace Transform Method

Thorwe¹

2012

AJCAM

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Partialintegro-differential equations (PIDE) occur naturally in various fields of science, engineering and social sciences. In this article, we propose a most general form of a linear PIDE with a convolution kernel. We convert the proposed PIDE to an ordinary differential equation (ODE) using a Laplace transform (LT). Solving this ODE and applying inverse LT an exact solution of the problem is obtained. It is observed that the LT is a simple and reliable technique for solving such equations. A variety of numerical examples are presented to show the performance and accuracy of the proposed method.

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Low-Dimensional Partial Integro-differential Equations for High-Dimensional Asian Options

Hepperger

2014

Inspired by Finance

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Hedging electricity swaptions using partial integro-differential equations

Cited by 13 publications

References 22 publications

Numerical Hedging of Electricity Contracts Using Dimension Reduction

Numerical Hedging of Electricity Contracts Using Dimension Reduction

Solving Partial Integro-Differential Equations Using Laplace Transform Method

Low-Dimensional Partial Integro-differential Equations for High-Dimensional Asian Options

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