René Aïd

A Structural Risk‐Neutral Model for Pricing and Hedging Power Derivatives

We develop a structural risk-neutral model for energy market modifying along several directions the approach introduced in Aid et al. In particular, a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus on pricing and hedging electricity derivatives. The hedging instruments are forward contracts on fuels and electricity. The presence of production capacities and electricity demand makes such a market incomplete. We follow a local risk minimization approach to price and hedge energy derivatives. Despite the richness of information included in the spot model, we obtain closed-form formulae for futures prices and semiexplicit formulae for spread options and European options on electricity forward contracts. An analysis of the electricity price risk premium is provided showing the contribution of demand and capacity to the futures prices. We show that when far from delivery, electricity futures behave like a basket of futures on fuels.

A STRUCTURAL RISK-NEUTRAL MODEL OF ELECTRICITY PRICES

The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamics of the electricity demand at the maturity T, and on the random available capacity of each production means. Our model explains, in a stylized fact, how the prices of different fuels together with the demand combine to produce electricity prices. This modeling methodology allows one to transfer to electricity prices the risk-neutral probabilities of the market of fuels and under the hypothesis of independence between demand and outages on one hand, and prices of fuels on the other hand, it provides a regression-type relation between electricity forward prices and forward prices of fuels. Moreover, the model produces, by nature, the well-known peaks observed on electricity market data. In our model, spikes occur when the producer has to switch from one technology to the lowest cost available one. Numerical tests performed on a very crude approximation of the French electricity market using only two fuels (gas and oil) provide an illustration of the potential interest of this model.

A probabilistic numerical method for optimal multiple switching problem and application to investments in electricity generation

In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the size of the local hypercubes involved in the regressions, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants. This model takes into account electricity demand, cointegrated fuel prices, carbon price and random outages of power plants. It computes the optimal level of investment in each generation technology, considered as a whole, w.r.t. the electricity spot price. This electricity price is itself built according to a new extended structural model. In particular, it is a function of several factors, among which the installed capacities. The evolution of the optimal generation mix is illustrated on a realistic numerical problem in dimension eight, i.e. with two different technologies and six random factors.In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the rate of convergence of the method in terms of the time step used to discretize the problem, of the regression basis used to approximate conditional expectations, and of the truncating time horizon. To make the method viable for problems in high dimension and long time horizon, we extend a memory reduction method to the general Euler scheme, so that, when performing the numerical resolution, the storage of the Monte Carlo simulation paths is not needed. Then, we apply this algorithm to a model of optimal investment in power plants in dimension eight, i.e. with two different technologies and six random factors.

Commodities, energy and environmental finance

Financialization of the Commodity Markets (R. Carmona).- Understanding the Tracking Errors of Commodity Leveraged ETFs (K. Guo, T. Leung).- Systemic Risk in Commodity Markets: What Do Trees Tell Us About Crises? (D. Lautier, J. Ling, F. Raynaud).- Margrabe Revisited (H. Tuenter).- Cross-Commodity Modelling by Multivariate Ambit Fields (F. Benth, A. Veraart, O. Barndorff-Nielsen).- Hedging Expected Losses on Derivatives in Electricity Futures Market (A. Nguyen Huu, N. Oudjane).- Calibration of Electricity Price Models (O. Feron, E. Daboussi).- Measuring the Competitiveness Benefits of Transmission Expansions in Wholesale Electricity Markets (F. Wolak).- Incorporating Managerial Information into Real Option Valuation (S. Jaimungal, Y. Lawryshyn).- Real Options with Regulatory Policy Uncertainty (M. Davison, C. Maxwell).- A Hedged Monte Carlo Approach to Real Option Pricing (E. Brigatti, M. Souza, J. Zubelli).- Technological Transition to Electric Mobility (R. Aid, I. Ben-Tahar).- Game Theoretic Models for Energy Production (M. Ludkovski, R. Sircar).- Design Analysis of Carbon Auction Market, Through Electricity Market Coupling (M. Bossy, N. Maizi, O. Pourtalier).- Dynamic Cournot Duopolies Under Stochastic Demand (M. Ludkovski, X. Yang).- Oligopoly Markets with Renewable Resources, Exploration and Evolving Extraction Costs with an Application to Energy Policy (A. Dasarathy, R. Sircar).In this work we are concerned with valuing optionalities associated to invest or to delay investment in a project when the available information provided to the manager comes from simulated data of cash flows under historical (or subjective) measure in a possibly incomplete market. Our approach is suitable also to incorporating subjective views from management or market experts and to stochastic investment costs. It is based on the Hedged Monte Carlo strategy proposed by Potters et al (2001) where options are priced simultaneously with the determination of the corresponding hedging. The approach is particularly well-suited to the evaluation of commodity related projects whereby the availability of pricing formulae is very rare, the scenario simulations are usually available only in the historical measure, and the cash flows can be highly nonlinear functions of the prices.

The coordination of centralised and distributed generation

This paper analyses the interaction between centralised carbon emissive technologies and distributed intermittent non-emissive technologies. In our model, there is a representative consumer who can satisfy her electricity demand by investing in distributed generation (solar panels) and by buying power from a centralised firm at a price the firm sets. Distributed generation is intermittent and induces an externality cost to the consumer. The firm provides non-random electricity generation subject to a carbon tax and to transmission costs. The objective of the consumer is to satisfy her demand while minimising investment costs, payments to the firm and intermittency costs. The objective of the firm is to satisfy the consumers residual demand while minimising investment costs, demand deviation costs, and maximising the payments from the consumer. We formulate the investment decisions as McKean-Vlasov control problems with stochastic coefficients. We provide explicit, price model-free solutions to the optimal decision problems faced by each player, the solution of the Pareto optimum, and the Stackelberg equilibrium where the firm is the leader. We find that, from the social planners point of view, the carbon tax or transmission costs are necessary to justify a positive share of distributed capacity in the long-term, whatever the respective investment costs of both technologies are. The Stackelberg equilibrium is far from the Pareto equilibrium and leads to an over-investment in distributed energy and to a much higher price for centralised energy.

Electricity Generation Technologies Systematic Risk

We propose a method to estimate differentiated costs of equity for electricity generation technologies. We provide evidence that there is a substantial difference in their cost of equity. This method is based on a regression between available information on electric utilities equity return and their electricity generation asset portfolio. Our first main finding is that there is a statistically significant risk premium for nuclear technology. This point is in line with the most recent studies using a higher discount rate for nuclear technology compared to coal fired plants. But, in contrast with these studies, we find that the value of the risk premium is on the order of 1% above the systematic risk of a coal-fired plant, which is considerably lower than their recommended value of 3%. The robustness of this result is tested for the structural breaks that may have been induced by the August, 2008 financial crisis and the Daishi-Fukushima accident of March, 2011. Our second finding deals with renewable energies. Despite the existence of subsidies through feed-in tariffs which would make them look like safe investments, they present a high level of systematic risk. A possible explanation for this important excess return is the fact that they are dependent on subsidies for their development and thus, bear a larger systematic exposure than can be seen on short term time series data.