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.]

Preview Full PDF 855 2251
Export citation
  • 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.

  • Keywords

Swing options jump-diffusion process mean-reverting Black-Scholes equation energy market partial integro-differential equation theta-method Implicit-Explicit-Scheme

  • AMS Subject Headings

65M10 91B25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{AAMM-4-259, author = {Mai Huong Nguyen and Matthias Ehrhardt}, 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 - Mai Huong Nguyen & Matthias Ehrhardt 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 KW - jump-diffusion process KW - mean-reverting KW - Black-Scholes equation KW - energy market KW - partial integro-differential equation KW - theta-method KW - 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
Copy to clipboard
The citation has been copied to your clipboard