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Modelling and Numerical Valuation of Power Derivatives in Energy Markets

Published online by Cambridge University Press:  03 June 2015

Mai Huong Nguyen  and
Matthias Ehrhardt
Mai Huong Nguyen*
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623 Berlin, Germany
Matthias Ehrhardt*
Affiliation:
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C-Mathematik und Naturwissenschaften, Bergische Universitaät Wuppertal, Gaußstr. 20, 42119 Wuppertal, Germany
*
Corresponding author. Email: [email protected]
Email: [email protected]

Abstract

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In this work we investigate the pricing of swing options in a model where the underlying asset follows a jump diffusion process. We focus on the derivation of the partial integro-differential equation (PIDE) which will be applied to swing contracts and construct a novel pay-off function from a tree-based pay-off matrix that can be used as initial condition in the PIDE formulation. For valuing swing type derivatives we develop a theta implicit-explicit finite difference scheme to discretize the PIDE using a Gaussian quadrature method for the integral part. Based on known results for the classical theta-method the existence and uniqueness of solution to the new implicit-explicit finite difference method is proven. Various numerical examples illustrate the usability of the proposed method and allow us to analyse the sensitivity of swing options with respect to model parameters. In particular the effects of number of exercise rights, jump intensities and dividend yields will be investigated in depth.

Keywords

65M1091B25Swing optionsjump-diffusion processmean-revertingBlack-Scholes equationenergy marketpartial integro-differential equationtheta-methodImplicit-Explicit-Scheme
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 3 , June 2012 , pp. 259 - 293
Copyright
Copyright © Global-Science Press 2012

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