The estimation of earthquakes’ occurrences prediction in seismic areas is a challenging problem in seismology and earthquake engineering. Indeed, the prevention and the quantification of possible damage provoked by destructive earthquakes are directly linked to this kind of prevision. In our paper, we adopt a parametric semi-Markov approach. This model assumes that a sequence of earthquakes is seen as a Markov process and besides it permits to take into consideration the more realistic assumption of events’ dependence in space and time. The elapsed time between two consecutive events is modeled as a general Weibull distribution. We determine then the transition probabilities and the so-called crossing states probabilities. We conclude then with a Monte Carlo simulation and the model is validated through a large database containing real data.

This article deals with the production of energy through photovoltaic (PV) panels. The efficiency and quantity of energy produced by a PV panel depend on both deterministic factors, mainly related to the technical characteristics of the panels, and stochastic factors, essentially the amount of incident solar radiation and some climatic variables that modify the efficiency of solar panels such as temperature and wind speed. The main objective of this work is to estimate the energy production of a PV system with fixed technical characteristics through the modeling of the stochastic factors listed above. Besides, we estimate the economic profitability of the plant, net of taxation or subsidiary payment policies, considered taking into account the hourly spot price curve of electricity and its correlation with solar radiation, via vector autoregressive models. Our investigation ends with a Monte Carlo simulation of the models introduced. We also propose the pricing of some quanto options that allow hedging both the price risk and the volumetric risk.

Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems’ output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR).

Since the liberalization of electricity markets, electricity prices are more volatile and expansion in electricity derivatives trading occurs. Indeed, a well-known feature of electricity prices concerns its high volatility. For this reason, operators use power futures to hedge against unexpected risk deriving from adverse fluctuations of spot prices within the planned delivering period. Indeed, futures contracts permit to fix the price of electricity in advance for the use in the scheduled period. Our paper is devoted specifically to the Italian electricity market. In this respect, we examine empirical data from IDEX, the Energy Derivatives part of the Italian derivatives market IDEM, administered by “Borsa Italiana.” We finally survey the possible connections concerning futures and spot prices and, as a consequence, we deduce information about important indicators whereof the ex-post risk premium and the net convenience yield. For this purpose, we use several regression techniques to determine suitable explanatory variables inherent the Italian market for the ex-post risk premium and the net convenience yield.

We introduce the industrial portfolio of a wind farm of a hypothetical company and its valuation consistent with the financial market. Next, we propose a static risk management policy originating from hedging against volumetric risk due to drops in wind intensity and we discuss the consequences. The hedging effectiveness firstly requires adequate modeling calibration and an extensive knowledge of these atypical financial (commodity) markets. In this hedging experiment, we find significant benefits for weather-sensitive companies, which can lead to new business opportunities. We provide a new financial econometrics approach to derive weather risk exposure in a typical wind farm. Our results show how accurate risk management can have a real benefit on corporate revenues. Specifically, we apply the spot market price simulation (SMaPS) model for the spot price of electricity. The parameters are calibrated using the prices of the French day-ahead market, and the historical series of the total hourly load is used as the final consumption. Next, we analyze wind speed and its relationship with electricity spot prices. As our main contribution, we demonstrate the effects of a hypothetical hedging strategy with collar options implemented against volumetric risk to satisfy demand at a specific time. Regarding the hedged portfolio, we observe that the “worst value” increases considerably while the earnings-at-risk (EaR) decreases. We consider only volumetric risk management, thus neglecting the market risk associated with electricity price volatility, allowing us to conclude that the hedging operation of our industrial portfolio provides substantial benefits in terms of the worst-case scenario.