GRUET Pierre

In this paper we study the calibration of specific multi-factorial Heath-Jarrow-Morton models to electricity market prices, with a focus on the estimation of the optimal number of factors. We describe a common statistical procedure based on likelihood maximisation and Akaike / Bayesian information criteria, in the case of calibration on futures prices, as well as on both spot and futures prices. We perform a detailed analysis on 6 European markets: Belgium, France, Germany, Italy, Switzerland and UK. The results show a lot of similarities on all the markets considered, especially on the optimal number of factors equal to 5. and on the behaviour of the different factors.

We statistically analyse a multivariate HJM diffusion model with stochastic volatility. The volatility process of the first factor is left totally unspecified while the volatility of the second factor is the product of an unknown process and an exponential function of time to maturity. This exponential term includes some real parameter measuring the rate of increase of the second factor as time goes to maturity. From historical data, we efficiently estimate the time to maturity parameter in the sense of constructing an estimator that achieves an optimal information bound in a semiparametric setting. We also identify nonparametrically the paths of the volatility processes and achieve minimax bounds. We address the problem of degeneracy that occurs when the dimension of the process is greater than two, and give in particular optimal limit theorems under suitable regularity assumptions on the drift process. We consistently analyse the numerical behaviour of our estimators on simulated and real datasets of prices of forward contracts on electricity markets. Mathematics Subject Classification (2010): 62M86, 60J75, 60G35, 60F05.

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We statistically analyse a multivariate HJM diffusion model with stochastic volatility. The volatility process of the first factor is left totally unspecified while the volatility of the second factor is the product of an unknown process and an exponential function of time to maturity. This exponential term includes some real parameter measuring the rate of increase of the second factor as time goes to maturity. From historical data, we efficiently estimate the time to maturity parameter in the sense of constructing an estimator that achieves an optimal information bound in a semiparametric setting. We also identify nonparametrically the paths of the volatility processes and achieve minimax bounds. We address the problem of degeneracy that occurs when the dimension of the process is greater than two, and give in particular optimal limit theorems under suitable regularity assumptions on the drift process. We consistently analyse the numerical behaviour of our estimators on simulated and real datasets of prices of forward contracts on electricity markets. Mathematics Subject Classification (2010): 62M86, 60J75, 60G35, 60F05.

We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and on the intraday price, typically due to error in the prediction of wind power generation. Finally, we solve the problem when taking into account delay constraints in thermal power production.

This thesis deals with the study of mathematical models of price movements in electricity markets, from the point of view of process statistics and stochastic optimal control. In the first part, we estimate the volatility components of a multidimensional diffusion process representing the evolution of prices on the electricity futures market. Its dynamics is driven by two Brownian motions. We seek to perform the estimation efficiently in terms of speed of convergence, and limit variance with respect to the parametric part of these components. This requires an extension of the usual definition of efficiency in the Cramér-Rao sense. Our estimation methods are based on the realized quadratic variation of the observed process. In the second part, we add model error terms to the observations of the previous model, to overcome the problem of overdetermination that arises when the dimension of the observed process is greater than two. The estimation techniques are still based on the realized quadratic variation, and we propose other tools to continue estimating the volatility components with the optimal speed in the presence of the error terms. Numerical tests are used to highlight the presence of such errors in our data. Finally, in the last part we solve the problem of a producer who intervenes on the intraday electricity market in order to compensate for the costs related to the random returns of his production units. Through his actions, he has an impact on the market. The prices and its anticipation of the demand of its consumers are modeled by a jumping diffusion. The tools of stochastic optimal control allow us to determine his strategy in an approximate problem. We give conditions for this strategy to be very close to optimality in the initial problem, and illustrate it numerically.

We consider the problem of optimal trading for a power producer in the context of intraday electricity markets. The aim is to minimize the imbalance cost induced by the random residual demand in electricity, i.e. the consumption from the clients minus the production from renewable energy. For a simple linear price impact model and a quadratic criterion, we explicitly obtain approximate optimal strategies in the intraday market and thermal power generation, and exhibit some remarkable properties of the trading rate. Furthermore, we study the case when there are jumps on the demand forecast and on the intraday price, typically due to error in the prediction of wind power generation. Finally, we solve the problem when taking into account delay constraints in thermal power production.

In this thesis, we study mathematical models for the representation of prices on the electricity markets, from the viewpoints of statistics of random processes and optimal stochastic control. In a first part, we perform estimation of the components of the volatility coefficient of a multidimensional diffusion process, which represents the evolution of prices in the electricity forward market. It is driven by two Brownian motions. We aim at achieving estimation efficiently in terms of convergence rate and, concerning the parametric part of those components, in terms of limit law. To do so, we must extend the usual notion of efficiency in the Cramér-Rao sense. Our estimation methods are based on realized quadratic variation of the observed process. In a second part, we add model error terms to the previous model, in order to care for some kind of degeneration occurring in it as soon as the dimension of the observed process is greater than two. Our estimation methods are still based on realized quadratic variation, and we give other tools in order to keep on estimating the volatility components with the optimal rate when error terms are present. Then, numerical tests provide us with some evidence that such errors are present in the data. Finally, we solve the problem of a producer, which trades on the electricity intraday market in order to cope with the uncertainties on the outputs of his production units. We assume that there is market impact, so that the producer influences prices as he trades. The price and the forecast of the consumers’ demand are modelled by jump diffusions. We use the tools of optimal stochastic control to determine the strategy of the producer in an approximate problem. We give conditions so that this strategy is close to optimality in the original problem, as well as numerical illustrations of that strategy.

This practical guide was written in collaboration with INERIS to help companies prevent the risks associated with worker exposure to electromagnetic fields. It aims to simplify the assessment process, based on an order of probability, by eliminating equipment that is immediately risk-free because it emits low-level electromagnetic fields. Once the simplified assessment has been completed, and depending on the equipment available in the company, an in-depth assessment is proposed, if necessary, for field sources of intermediate intensity. It appears that eight industrial applications are mainly likely to expose operators. These eight applications are followed as a common thread throughout the different parts of this book. The main actions for reducing exposure are listed, and employee information and training, accessibility of risk assessment and employee health surveillance are discussed.