The challenge in modelling electricity prices is mainly caused by it’s non-storability. Spot prices are thus determined by the current demand/supply interaction, but hardly by expectations about the future. They show characteristics as mean-reversion, seasonal patterns, an immense volatility and spikes, which cannot be captured with standard stock market models. On contrary, there exists growing markets, where financial futures contracts are traded. These contracts are storable and show similar characteristics to other financial assets. In particular they feature a significant lower volatility then spot prices. Moreover, the volatility is decreasing in the time to maturity.

This paper develops and applies a novel estimation procedure for quantile regressions with time-varying coefficients based on a fully parametric, multifactor specification. The algorithm recursively filters the multifactor dynamic coefficients with a Kalman filter and parameters are estimated by maximum likelihood. The likelihood function is built on the Skewed-Laplace assumption. In order to eliminate the non-differentiability of the likelihood function, it is reformulated into a non-linear optimization problem with constraints. A relaxed problem is obtained by moving the constraints into the objective, which is then solved numerically with the Augmented Lagrangian Method. In the context of an application to electricity prices, the results show the importance of modelling the time-varying features and the explicit multi-factor representation of the latent coefficients is consistent with an intuitive understanding of the complex price formation processes involving fundamentals, policy instruments and participant conduct. We demonstrated the value of a well specified dynamic model for quantile estimation by means of an application to electricity price risk. Electricity prices are a commodity in which price formation is nonlinear in its relationship to fundamentals, dynamic in the relative influences of drivers, with further complications introduced by policy interventions for supporting specific technologies and opportunities for participant conduct to be influential at high and low prices. Despite these complications careful consideration of the shape of the supply function with its concave, flat and convex regions, together with the information that is available to market participants day ahead allows plausible expectations for the price dynamics to be considered, and these explain very well the signs and significance of the parameters in the estimated models. Nevertheless, the models need to have a detailed specification with the various quantiles being related to multiple factors through coefficients which have dynamic properties themselves related to some of the exogenous factors. This modelling requirement motivates the development of quantile models that need fully parametric specifications to capture dynamics through exogenous factors and time-varying coefficients. A novel general methodology has therefore been developed in which time-varying multi factor coefficients are recursively estimated with a Kalman filter using maximum likelihood. Since the likelihood function is non-differentiable, the problem is re-formulated as a non-linear optimization with constraints, and furthermore re-formulated again by moving the constraints into the objective function to solve an augmented Lagrangian method. With careful selection of starting values, maximum likelihood estimates were thereby acquired. As a general approach, we would expect this to be useful in many applications of risk management and quantile estimation where there is dynamic complexity in price formation and plausible exogenous price drivers.

Environmental regulations force car manufacturers to renew the powertrain technology portfolio offered to the customer to comply with greenhouse gas emission targets. In turn, automotive companies face the task of identifying the “right” powertrain technology portfolio consisting of, e.g., internal combustion engines and electric vehicles, because the selection of a particular powertrain technology portfolio affects different company targets simultaneously. What makes this decision even more challenging is that future market shares of the different technologies are uncertain. Our research presents a new decision-support approach for assembling optimal powertrain technology portfolios while making decision-makers aware of the trade-offs between the achievable profit, the achievable market share, the market share risk, and the greenhouse gas emissions generated by the selected vehicle fleet. The proposed approach combines “a posteriori” decision-making with multi-objective optimization. In an application case, we feed the outlooks of selected market studies into the proposed decision-support system. The result is a visualization and analysis of the current real-world decision-making problem faced by many automotive companies. Our findings indicate that for the proposed greenhouse gas restriction at work in 2030 in the European Union, no optimal powertrain technology portfolio with less than 35% of vehicles equipped with an electric motor exists.

We propose a novel regime-switching approach for modeling electricity spot prices that takes into account the relation between spot and forward prices. Additionally the model is able to reproduce spikes and negative prices. Market prices are based on an observed forward curve. We distinguish between a base regime and an upper as well as a lower spike regime. The model parameters are calibrated using historical hourly price forward curves for EEX Phelix and the dynamics of hourly spot prices. The model is compared with common time series approaches like ARMA and GARCH.

We propose a novel regime-switching approach for the simulation of electricity spot prices that is inspired by the class of fundamental models and takes into account the relation between spot and forward prices. Additionally the model is able to reproduce spikes and negative prices. Market prices are derived given an observed forward curve. We distinguish between a base regime and an upper as well as a lower spike regime. The model parameters are calibrated using historical hourly price forward curves for EEX Phelix and the dynamic of hourly spot prices. We further evaluate different time series models such as ARMA and GARCH that are usually applied for modeling electricity prices and conclude a better performance of the proposed regime-switching model.

We propose a novel regime-switching approach for the simulation of electricity spot prices that is inspired by the class of fundamental models and takes into account the relation between spot and forward prices. Additionally the model is able to reproduce spikes and negative prices. Market prices are derived given an observed price forward curve, and spikes may occur with a certain probability. To this end, we distinguish between a base regime and an upper as well as a lower spike regime. The model parameters are calibrated using the historical hourly price forward curves for EEX Phelix and the dynamics of hourly spot prices. We further evaluate different time series models such as ARMA and GARCH that are usually applied for modeling electricity prices and conclude a better performance of the proposed regime-switching model.

A bank's financial management faces various sources of uncertainty when funds from savings account deposits are invested in the marketplace. Future interest rates are unknown and customers are allowed to withdraw their deposits at any point in time. The objective is to find a portfolio of fixed income instruments that maximizes the bank's interest surplus from the investment of funds and to manage the prepayment risk inherent to non-maturing accounts. A multistage stochastic programming model is presented that takes into account the uncertain evolution of interest rates and volume. A case study based on interest rate data of a 7 years period indicates that the surplus can be increased by 25 basis points compared to the static approach formerly used, while volatility is reduced significantly.

We formulate the service composition problem as a multi-objective stochastic program which simultaneously optimizes the following quality of service (QoS) parameters: workflow duration, service invocation costs, availability, and reliability. All of these quality measures are modelled as decision-dependent random variables. Our model minimizes the average value-at-risk (AVaR) of the workflow duration and costs while imposing constraints on the workflow availability and reliability. AVaR is a popular risk measure in decision theory which quantifies the expected shortfall below some percentile of a loss distribution. By replacingthe random durations and costs with their expected values, our risk-aware model reduces to the nominal problem formulation prevalent in literature. We argue that this nominal model can lead to overly risky decisions. Finally, we report on the scalability properties of our model.