Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis

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Numerical Methods for Pricing Swing Options in the Electricity Market


Master's Thesis in Financial Mathematics, Halmstad University, Sweden


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Description

Since the liberalisation of the energy market in Europe in the early 1990s, much opportunity to trade electricity as a commodity has arose. One significant consequence of this movement is that market prices have become more volatile instead of its tradition constant rate of supply. Spot price markets have also been introduced, affecting demand of electricity as companies now have the option to not only produce their own supply but also purchase this commodity from the market. Following the liberalisation of the energy market, hence creating a greater demand for trading of electricity and other types of energy, various types of options related to the sales, storage and transmission of electricity have consequently been introduced.

Particularly, swing options are popular in the electricity market. As we know, swing type of derivatives are given in various forms and are mainly traded as over-the-counter contracts at energy exchange. These options offer flexibility with respect to timing and quantity.

Tradtionally, the Geometric Brownian Motion (GBM) model is a very popular and standard approach for modelling the risk neutral price dynamics of underlyings. However, a limitation of this model is that it has very few degrees of freedom, which dos not capture the complex behaviour of electricity prices. In short the GBM model is inefficient in the pricing of options involving electricity. Other models have subsequently been used to bridge this inadequecy, e.g. the spot price models, futures price models, etc.

To model risk-neutral commodity prices, there are basically two different methodologies, namely spot and futures or so-called term structure models. As swing options are usually written on spot prices, it is important for us to examine these models in order to more accurately inculcate their effect on the pricing of swing options.

In this thesis, we aim to examine the pricing of swing options in the electricity market. We will consider some existing price models and to calibrate the prices of swing options in comparison.

Keywords

References:

  1. A. Bodea, Valuation of Swing Options in Electricity Commodity Markets , Dissertation, University of Heidelberg, 2012.
  2. A. Barbieri and M.B. Garman Understanding the Valuation of Swing Contracts, Energy and Power Risk Management, October 1996.
  3. R. Carmona and M. Ludkovski, Gas storage and supply guarantees: an optimal switching approach, Working Paper, Princeton University, 2005.
  4. R. Carmona and N. Touzi, Optimal Multiple Stopping and Valuation of Swing Options, Math. Finance 18 (2008), 239-268.
  5. R. Carmona and S. Dayanik, Optimal multiplestopping of linear diffusions and swing options, Math. Oper. Res. 33 (2008), 446-460.
  6. L. Clewlow and C. Strickland, Energy Derivatives: Pricing and Risk Management, Lacima Publications, 2000.
  7. M. Davison and L. Anderson, Approximate recursive valuation of electricity swing options, Technical Report, The University of Western Ontario, 2003.
  8. S. Deng, B. Johnson and A. Sogomonian, Exotic electricity options and the valuation of electricity generation and transmission assets, Decision Support Systems 30 (1998), 383-392.
  9. Y. d'Halluin, P.A. Forsyth and K.R. Vetzal, Numerical methods for contingent claims under jump diffusion processes,, IMA J. Numer. Anal. 25 (2005), 87-112.
  10. U. Dörr, Valuation of Swing Options and Examination of Exercise Strategies with Monte Carlo Techniques, Master thesis, University of Oxford, 2003.
  11. J. Doege, P. Schiltknecht and H.-J. Lüthi, Risk management of power portfolios and valuation of flexibility, OR Spectrum 28 (2006), 267-287.
  12. D.J. Duffy, Numerical Analysis of Jump Diffusion Models: A Partial Differential Equation Approach, Working Paper, 2004.
  13. A. Eydeland and H. Geman, Fundamentals of electricity derivatives, in: Energy modelling & the management of uncertainty, Risk Publications, London, (1999), pp. 35-43.
  14. S.-E. Fleten and J. Lemming, Constructing forward price curves in electricity markets, Energy Economics 25 (2003), 409-424.
  15. M.B. Garman and A. Barbieri, Ups and Down of Swing, Energy and Power Risk Mangement, 1997.
  16. A. Ibáñez, Valuation by simulation of contingent claims with multiple exercise opportunities, Math. Finance 14 (2004), 223-248.
  17. P. Jaillet, E.I. Ronn and S. Tompaidis, Valuation of Commodity-Based Swing Options, Management Science 50 (2004), 909-921.
  18. V. Kaminski and S. Gibner, Exotic options, in: Managing Energy Price Risk, V. Kaminski (ed.), Risk Publications, London, pp. 117-148.
  19. V. Kaminski, The challenge of pricing and risk managing electricity derivatives, in: The US power market, Risk Publications, London, (1997), pp. 149-171.
  20. J. Keppo, Pricing of electricity swing options, J. Derivatives 2 (2004), 26-43.
  21. M. Kjaer, The pricing of swing options in a mean-reverting model with jumps, Applied Mathematical Finance, 2007.
  22. M. Kloimwieder, Swing Options in Electricity Markets, Masters Thesis, University of Oxford, 2003.
  23. T. Kluge, Pricing Swing Options and other Electricity Derivatives, Ph.D. Thesis, University of Oxford, 2006.
  24. A. Lari-Lavassani, M. Simchi and A. Ware, A Discrete Valuation of Swing Options, Canadian Appl. Math. Quarterly 9 (2001), 35-73.
  25. J.J. Lucia and E.S. Schwartz, Electricity Prices and Power Derivatives: Evidence from the Nordic Power Exchange, Review Deriv. Research 5 (2002), 5-50.
  26. A. Mayo, Methods for the rapid solution of the pricing PIDEs in exponential and Merton models, J. Comput. Appl. Math. 222 (2008), 128-143.
  27. N. Meinshausen and B. Hambly, Monte Carlo methods for the valuation of multiple exercise options, Math. Finance 14 (2004), 557-583.
  28. J. Meyer, Valuation of Energy Derivatives with Monte Carlo Methods, Masters Thesis, University of Oxford, 2004.
  29. D. Pilipovic, Energy Risk: Valuing and Managing Energy Derivatives, McGraw-Hill, 1998.
  30. D. Pilipovic and J. Wengler, Getting into the swing, Energy and Power Risk Management 2 (1998).
  31. H. Siede, Multi-Period Portfolio Optimization, PhD thesis, University of St. Gallen, 2000.
  32. A.C. Thompson, Valuation of Path-Dependent Contingent Claims with Multiple Exercise Decisions over Time: The Case of Take-or Pay, J. Financial Quantitative Analysis 30 (1995), 271-293.
  33. M. Thompson, M. Davison and H. Rasmussen, Valuation and optimal operation of electric power plants in competitive markets, Operations Research 52 (2004), 546-562.
  34. T. Wegner, Swing options and seasonality of power prices, Master thesis, University of Oxford, 2002.
  35. M. Wilhelm, Modelling, Pricing and Risk Management of Power Derivatives, Ph.D. Thesis, ETH Zürich, 2007.

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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