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Volume 4, Issue 3
Modelling and Numerical Valuation of Power Derivatives in Energy Markets

Mai Huong Nguyen & Matthias Ehrhardt

Adv. Appl. Math. Mech., 4 (2012), pp. 259-293.

Published online: 2012-04

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • AMS Subject Headings

65M10, 91B25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-259, author = {Nguyen , Mai Huong and Ehrhardt , Matthias}, title = {Modelling and Numerical Valuation of Power Derivatives in Energy Markets}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {3}, pages = {259--293}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m1133}, url = {http://global-sci.org/intro/article_detail/aamm/119.html} }
TY - JOUR T1 - Modelling and Numerical Valuation of Power Derivatives in Energy Markets AU - Nguyen , Mai Huong AU - Ehrhardt , Matthias JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 259 EP - 293 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m1133 UR - https://global-sci.org/intro/article_detail/aamm/119.html KW - Swing options, jump-diffusion process, mean-reverting, Black-Scholes equation, energy market, partial integro-differential equation, theta-method, Implicit-Explicit-Scheme. AB -

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.

Mai Huong Nguyen & Matthias Ehrhardt. (1970). Modelling and Numerical Valuation of Power Derivatives in Energy Markets. Advances in Applied Mathematics and Mechanics. 4 (3). 259-293. doi:10.4208/aamm.10-m1133
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