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


Swing Options and Least-Square Monte Carlo Techniques

Bachelorarbeit Wirtschaftsmathematik



The new development of modern communications and transportation technology simplifies the trading of commodities, but at the same time, also brings more risk, such as extreme price volatility and sudden consumption fluctuation etc. Especially for those commodities, which are difficult or very expensive to be stored, for example electricity or some other commodities in energy markets. In order to hedge themselves against such risk, many consumers enter into forward contracts which give them the right and the obligation to purchase a fixed amount of the commodity for a predetermined price. But it is not enough to solve such storage problem, since the consumers do not know their exact future need of the commodity. Therefore so-called swing contracts have been developed in order to give the holder certain flexibility with respect to the amount purchased in the future. A swing option allows the holder to buy or sell a certain quantity of the underlying for a predefined price. The particular suitability lies in the fact that the holder is allowed to perform a certain number of those up-swings and down-swings during the options life (flexibility-to-deliver feature), providing the possibility to react to unexpected changes in supply and demand of energy. These options can be endowed with restrictions concerning the total amount taken by the holder, and also be associated with penalties in case the volume exceeds predefined limits (take-or-pay feature). This bachelor thesis focus on the valuation of swing options using the extended Least-Squares Monte Carlo algorithm based on Longstaff and Schwartz method. In the next chapter we will present a brief introduction to swing option, which contains the main idea about swing options and how the spot price be modeled by one factor mean-reverting process. The second chapter focuses on the Least-Squares Monte Carlo method, theory, algorithm and a simplified illustrative example will be introduced.


swing options, least squares Monte Carlo method


MATLAB codes are freely available as part of the Computational Finance Toolbox at the University of Wuppertal.


  1. U. Dörr, Valuation of Swing Options and Examination of Exercise Strategies by Monte Carlo Techniques, Master thesis in Mathematical Finance, University of Oxford, 2003.
  2. N. Broussev, G.Ch. Pflug, Swing Options in Electricity Markets; Behavioural Models and Pricing, Institut für Statistik und Decision Support Systems der Universität Wien, 2006.
  3. F.A. Longstaff, E.S. Schwartz, Valuing American options by simulation: A simple least-squares approach, Rev. of Fin. Studies, 14 (2001).
  4. J.J. Lucia, E.S. Schwartz, Electricity prices and power derivatives: Evidence from the Nordic power exchange, Rev. Deriv. Research, 5 (2002).
  5. P. Jeillet, E.I. Ronn, and S. Tompaidis, Valuation of Commodity-Based Swing Options, Management Science 50 (2004), 909-921.
  6. T. Wegner, Swing Options and Seasonality of Power Prices, Masters Thesis, University of Oxford, 2002.

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

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