White noise approach to parabolic stochastic partial differential equations

A certain dass of stochastic partial differential equations of parabolic type is studied within white noise analysis

Stochastic volatility, jumps and leverage in energy and stock markets : evidence from high frequency data

The study of volatility in crude oil and natural gas markets and its interac- tion with returns (leverage) has a broad range of financial impacts both from a hedging point of view and also for forecasting purposes.The main limitation of using daily data is that volatility is not observable. In contrast, intra-day data provide an almost continuous observation of the return series, making volatility observable. From an econometric point of view, the employment of intra-day data leads to the estimation of structural parameters of stochastic volatility models using simple moment conditions while fitting all the relevant empirical features of energy and stock index returns. This paper contributes to the current debate by: 1) exploring evidence of leverage effects and jumps in energy futures markets versus financial stock indexes (S&P500) and 2) evalu- ating the impact of leverage on risk forecasting in a VaR and CVaR sense. We find significant evidence of a leverage effect for S&P500 and crude oil markets: a negative shock to returns increases volatility in these markets. We also find evidence of an inverse leverage effect for the natural gas market: volatility becomes higher when energy returns increase. We also find evidence for jumps in the energy futures markets. We show that the introduction of leverage improves the forecasting ability of the SV model using the RMSE and MAE criteria for all the markets considered while introducing jumps improves only the ability of modeling the behaviour of the volatility for the crude oil futures market

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Pricing Futures and Options in Electricity Markets

In this paper we derive power futures prices from a two-factor spot model being a generalization of the classical Schwartz–Smith commodity dynamics. We include non-Gaussian effects by introducing Lévy processes as the stochastic drivers, and estimate the model to data observed at the European Electricity Exchange in Germany. The spot and futures price models are fitted jointly, including the market price of risk parameterized from an Esscher transform. We apply this model to price call and put options on power futures. It is argued theoretically that the pricing measure for options may be different to the pricing measure of futures from spot in power markets due to the non-storability of the electricity spot. Empirical evidence pointing to this fact is found from option prices observed at the European Electricity Exchange. The definitive version is available at springerlink.co