In portfolio theory, the most commonly used model for estimating the value of an option is the Black and Scholes model [1]. This model is based upon the assumptions of modern portfolio theory, where prices reflect all the available information. The Black and Scholes model gives the value of an option as a function of the spot price and the volatility of the underlying asset, the strike price, the time and the risk free rate. It is suitable for European options, while the estimation of an American option will require in addition to estimate the likelihood of early exercise (generally resulting from discontinuity events such as dividend distribution or bankruptcy).

Option pricing in energy markets raises specific issues, due to difficult storage and the existence of spot price models [2,3]. For this reason, the time of exercise is a much more crucial parameter than in financial markets, and can be negotiated between the parties. Therefore, European and American options shall be treated separately. European options can be priced by predicting a spot price and using an approach similar to the Black and Scholes model. For American options, the Black and Scholes equation becomes an inequality which solution can be approximated by robust optimization models [4,5].

[1] The Pricing of Options and Corporate Liabilities, Fischer Black and Myron Scholes, Journal of Political Economy, Vol. 81, No. 3 (May - Jun., 1973), pp. 637-654.

[2] ELECTRICITY MARKET DESIGN: Energy Trading Practice and Market Manipulation Theory, William W. Hogan, 7th Annual Nodal Trader Conference, New York, NY, October 9, 2014.

[3] Modeling and evaluating electricity options markets with intelligent agents, Lane, D.W.; Richter, C.W., Jr.; Sheble, G.B., International Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2000.

[4] Electricity derivatives and risk management, S.J. Deng, S.S. Oren, Energy, Volume 31, Issues 6–7, May–June 2006, Pages 940–953.

[5] Energy and Power Risk Management, New developments in Modeling, Pricing, and Hedging, Alexander Eydeland and Krzysztof Wolniec, Wiley, 2003.

**Contributor**

Dr Philippe Ezran, Large Networks and Systems Group (LANEAS)

Prof. Julis Zilinskas, Vilnius University

Dr. Andrea Cassioli, Ecole Polytechnique (Paris, France)

Dr. Yoram Haddad, Jerusalem College of Technology