5. Measuring Model Risk in the European Energy
5.6 Conclusions and Future Research
We provide for the first time an empirical assessment of model risk in the German wholesale
electricity market implementing a quantitative measure of model risk for VaR, proposed by Barrieu and Scandolo (2015). The German electricity market has undergone deep structural changes as the modification of the generation mix required to reduce carbon emissions, and this has increased the complexity of the energy sector and affected the stochastic nature of electricity prices, which are characterized by new empirical distributional shapes. Therefore, relaxing the assumption of normality and using a wide range of alternative distributions, we have quantified model risk under the well- established setting of GARCH models.
These results emphasize that the distributional assumptions made in price modelling can produce a relevant difference and then trigger substantial model risk. In this specific case, rolling measures, computed with respect to the normal distribution, exhibit average values very close to one for more recent years; hence, indicating full model risk.
Indeed, it is interesting to observe that there has been a progressive increase in model risk from 2007. This may be explained looking at the evolution of the German generation mix, and analyzing the data collected from ENTSO–E.8 Figures 5.5 and 5.6 clearly show the important transformations
occurred in this power market: starting from 2007 there has been a progressive reduction of nuclear generation, and a pretty constant generation from hydro, but an increasing share of wind together with a substantial amount of electricity produced by solar. Furthermore, it is important to recall that the negative pricing has been introduced on the intra–day market in 2007 and on the day–ahead
German/Austrian market in 2008; and this has substantially modified the empirical properties of hourly electricity prices, and consequently daily average prices.
Fig. 5.5 German generation mix over years
Fig. 5.6 German RES mix over years
Although our results can be considered an exploration, they clearly show that the increasing complexity of market mechanisms and their regulation, together with the introduction of new
fundamental drivers as renewable energy sources (specifically wind and solar), have dramatically modified the nature and statistical properties of electricity prices. Indeed, we document a progressive increase of model risk with the time–evolution of the generation mix, and under three different
assumptions for the reference model. This fact highlights the importance of considering the impact that the model choice has on risk assessment, particularly when operating in complex markets such as the energy ones.
To this aim, this analysis can be considered “preliminary” and future developments will address at least two issues. First, we plan to extract a “net model risk” by explicitly modelling, hence
excluding, other sources of risks such as the demand, RES-induced, and fundamental risks related to fuels. Second, we aim at implementing a more flexible methodology which takes into account time- varying moments depending on plausible energy risk factors. We have explored the great potential of a recent methodology (the generalized additive models for location, scale and shape, GAMLSS9), encompassing equations for location, scale and shape. Indeed, we have considered the simplest formulation with constant variance, skewness and kurtosis in a preliminary analysis, and results on RMMR obtained within this framework recall the dynamics of those obtained with the GARCH models, hence providing the same qualitative indications even if with obvious different magnitudes due to differences in model formulations.10 Clearly, we expect to get a better picture of the model risk once the other sources of electricity risk are explicitly included in this more flexible framework, and once an autoregressive structure is adopted in the equations of all four moments.
To conclude, we have emphasized that the risk quantification of a financial position crucially depends on the employed model. If a set of alternative models is fixed, including all possible
distributions that is meaningful to consider, then the measure of model risk we have considered can
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give useful indications about the model which is currently implemented (i.e. the reference one). If RMMR has been consistently close to 1 in the recent period, then it is likely that VaR will be
underestimated in the subsequent days, if we use the reference model. In this case, proper actions can be taken, such as incrementing the VaR figure by an amount that depends on model risk. In practice, implementing sophisticated models can be costly, for instance, in terms of IT equipments, estimation times, and need of skilled employees. In view of these considerations, the measure of model risk could be computed for a limited amount of time and from time to time. Still, this would provide risk managers with a useful figure that could be complementary to the usual back-testing results for VaRs.
Acknowledgements
We thank two anonymous referees who helped us to improve the paper. Furthermore, the first author acknowledges the European financial support under the scheme Marie Curie Actions, Intra–
European Fellowship for Career Development (FP7–PEOPLE–2011–IEF) for AaDAMS.
References
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R.A. Rigby, D.M. Stasinopoulos, Generalised additive models for location, scale and shape (with discussion). Appl. Stat. 54 1–38, (2005) S.S. Shapiro, R.S. Francia, An approximate analysis of variance test for normality. J. Am. Stat. Assoc. 67, 215–216 (1972)
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Footnotes
The volatility dynamics within energy markets has been extensively studied and modelled by using GARCH–type models, see for instance Fan et al. (2008) who measured risk for both the WTI and Brent crude oil spot markets using the generalized error distribution (GED) to estimate the extreme downside and upside VaR of oil price returns.
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This new empirical fact is even more evident when hourly prices are considered; and less so, when day-ahead prices are computed as arithmetic mean of 24 hourly prices.
Electricity prices are affected by different forms of seasonality: as the intra–daily one (for night–time and day–time), weekly
seasonality reflecting no business activities during weekends; and the more general calendar seasonality, with summers characterized by high electricity demand for air conditioning. Whereas, spikes are abnormal upward and downward price movements.
For the densities of these distributions please refer to Ghalanos (2014).
In general, there will be a parameter that controls for skewness and/or one that controls for kurtosis. We denote them, respectively, ν and τ across different families. The family GHYP has a third parameter, that we denote λ.
See Ghalanos (2014) for details.
However, we point out that in GARCH models with normal innovations, the variables X t themselves are not normal, as they always display extra-kurtosis.
ENTSO-E is the European network of transmission system operators for electricity. More information can be found at www.entsoe.
eu.
See Rigby and Stasinopoulos (2005) for a full description with all details.
These results rely on a structure which is simpler than the one presented in this paper, because of the constant higher moments opposite to the time-varying volatility of the GARCH framework. Among other differences, we refer for instance to the linearities between the equations of sample moments, and the presence/absence of their autoregressive structures. These results are available on request.
Part II
Pricing and Valuation
(1) (2) (3)
© Springer International Publishing AG 2018
Giorgio Consigli, Silvana Stefani and Giovanni Zambruno (eds.), Handbook of Recent Advances in Commodity and Financial Modeling, International Series in Operations Research & Management Science 257, https://doi.org/10.1007/978-3-319-61320-8_6