Modeling, pricing and risk management of power derivatives

Abstract

Deregulation of energy markets has necessitated the adoption of risk management techniques in the power industry. The launched liberalization and therewith the uncertainty involved in gas, fuel and electrical power prices requires an efficient management of production facilities and financial contracts. Thereby derivatives build essential instruments to exchange volume as well as price risks. However, the valuation of financial derivatives in power markets has proven to be particularly challenging. The fact that electrical power is not physically storable eliminates the direct application of the no–arbitrage methodology from financial mathematics. Consequently, new approaches are required to value even the simplest derivative products in electricity markets. That is, modeling arbitrage–free electricity price dynamics turns out to be the crucial step towards fair pricing of financial products in power markets. In this work we propose an approach, which converts an electricity market into a virtual base market consisting of zero bonds and an additional risky asset. Using this structure, interest rate theory as well as the change–of–numeraire technique are applied to elaborate risk neutral price dynamics in electricity markets. As a result, explicit formulas are obtained for European type derivatives such as spread, cap, floor and collar options. Through the performed historical calibration it can be seen that in the proposed model, contract volatilities close to maturity increase significantly. For valuing swing type derivatives, which possess no closed–form solutions, an algorithm based on finite element methods is proposed. Thereby the reduction of multiple stopping time problems to a cascade of single stopping time problems is utilized. The obtained numerical results for different swing options all show a smooth and stable behavior. This allows an interpretation of the optimal exercise boundary and an analysis of the dependence of swing option prices on initial spot prices and on the number of exercise rights. A comparison of the finite element algorithm to Monte Carlo methods demonstrates the strengths of the developed numerical procedure.