We introduce a new and highly tractable structural model for spot and derivative prices in electricity markets. Using a stochastic model of the bid stack, we translate the demand for power and the prices of generating fuels into electricity spot prices. The stack structure allows for a range of generator efficiencies per fuel type and for the possibility of future changes in the merit order of the fuels. The derived spot price process captures important stylized facts of historical electricity prices, including both spikes and the complex dependence upon its underlying supply and demand drivers. Furthermore, under mild and commonly used assumptions on the distributions of the input factors, we obtain closed-form formulae for electricity forward contracts and for spark and dark spread options. As merit order dynamics and fuel forward prices are embedded into the model, we capture a much richer and more realistic dependence structure than can be achieved by classical reduced-form models. We illustrate these advantages by comparing with Margrabe's formula and a simple cointegration model, and highlight important implications for the valuation of power plants.Electricity markets and structural model and forward prices and spread options and power plant valuation JEL Classification Numbers: C60, G12, G13, Q40Partially supported by NSF -DMS-0739195. 1 arXiv:1205.2299v1 [q-fin.PR] 10 May 20121 Alternatively, firms may, in some markets, submit continuous bid curves, which map an amount of electricity to the price at which it is offered. For our purposes this distinction will however not be relevant.2 This description is of course a simplification of the market administrator's complicated unit commitment problem, typically solved by optimization in order to satisfy various operational constraints of generators, as well as transmission constraints. Details vary from market to market and we do not address these issues here, as our goal is to approximate the price setting mechanism and capture the key relationships needed for derivative pricing.ORFE,

Abstract. The goal of this survey is to review the major idiosyncrasies of the commodity markets and the methods which have been proposed to handle them in spot and forward price models. We devote special attention to the most idiosyncratic of all: electricity markets. Following a discussion of traded instruments, market features, historical perspectives, recent developments and various modeling approaches, we focus on the important role of other energy prices and fundamental factors in setting the power price. In doing so, we present a detailed analysis of the structural approach for electricity, arguing for its merits over traditional reduced-form models. Building on several recent articles, we advocate a broad and flexible structural framework for spot prices, incorporating demand, capacity and fuel prices in several ways, while calculating closed-form forward prices throughout.

These results demonstrate the importance of the surface morphology created during the vial forming process. Given the diferences observed, final vial selection should include extensive microscopical and product stress testing studies on multiple vial lots.

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