Due to significant variances in data granularity between the Standard Formula and an internal model, a magnitude of difference can exist between the two approaches when calculating solvency capital, with potentially lower SCR calculations for the cat component when using an internal model. The application of Solvency II is, however, not all about capital estimation, but also relates to effective risk management processes embedded throughout an organization.
Implementing cat models fully into the internal model process, as opposed to just relying only on cat model loss output, can introduce significant improvements to risk management processes.
Infrastructure Investments: the Impact on Solvency II Balance Sheets for Insurers
Cat models provide an opportunity to improve exposure data quality and allow model users to fully understand the benefits of complex risk mitigation structures and diversification. Catastrophe model vendors are therefore obliged to help users understand underlying assumptions and their inherent uncertainties, and provide them with the means of justifying model selection and appropriateness.
Insurers have benefited from RMS support to fulfil these requirements, offering model users deep insight into the underlying data, assumptions, and model validation, to ensure they have complete confidence in model strengths and limitations. As always, the risk is particularly uncertain, and with Solvency II due smack in the middle of the season, there is greater imperative to really understand the uncertainty surrounding the peril—and manage windstorm risk actively. Business can benefit, too: new modeling tools to explore uncertainty could help re insurers to better assess how much risk they can assume, without loading their solvency capital.
The variability of European windstorm seasons can be seen in the record of the past few years. Though insured losses were moderate, had their tracks been different, losses could have been so much more severe. In contrast, was busy. The intense rainfall brought by some storms resulted in significant inland flooding, though wind losses overall were moderate, since most storms matured before hitting the UK. These two storms were outliers during a general lull of European windstorm activity that has lasted about 20 years.
Spiky losses like Niklas could occur any year, and maybe in clusters , so it is no time for complacency.
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The unpredictable nature of European windstorm activity clashes with the demands of Solvency II , putting increased pressure on re insurance companies to get to grips with model uncertainties. Under the new regime, they must validate modeled losses using historical loss data. That is simply too little loss information to validate a European windstorm model, especially given the recent lull, which has left the industry with scant recent claims data.
That exacerbates the challenge for companies building their own view based only upon their own claims. The model includes the most up-to-date long-term historical wind record, going back 50 years, and incorporates improved spatial correlation of hazard across countries together with a enhanced vulnerability regionalization, which is crucial for risk carriers with regional or pan-European portfolios.
For Solvency II validation, it also includes an additional view based on storm activity in the past 25 years. Windstorm clustering—the tendency for cyclones to arrive one after another, like taxis—is another complication when dealing with Solvency II. It adds to the uncertainties surrounding capital allocations for catastrophic events, especially due to the current lack of detailed understanding of the phenomena and the limited amount of available data. To chip away at the uncertainty, we have been leading industry discussion on European windstorm clustering risk, collecting new observational datasets, and developing new modeling methods.
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We plan to present a new view on clustering, backed by scientific publications, in These new insights will inform a forthcoming RMS clustered view, but will be still offered at this stage as an additional view in the model, rather than becoming our reference view of risk. We will continue to research clustering uncertainty, which may lead us to revise our position, should a solid validation of a particular view of risk be achieved. The scientific community is still learning what drives an active European storm season.
Some patterns and correlations are now better understood , but even with powerful analytics and the most complete datasets possible, we still cannot yet forecast season activity. However, our recent model update allows re insurers to maintain an up-to-date view, and to gain a deeper comprehension of the variability and uncertainty of managing this challenging peril.
That knowledge is key not only to meeting the requirements of Solvency II, but also to increasing risk portfolios without attracting the need for additional capital. It can improve a wide range of risk management decisions, from basic geographical risk diversification to more advanced deterministic and probabilistic modeling. The need to capture and use high quality exposure data is not new to insurance veterans. The underlying logic of this principle is echoed in the EU directive Solvency II, which requires firms to have a quantitative understanding of the uncertainties in their catastrophe models; including a thorough understanding of the uncertainties propagated by the data that feeds the models.
The implementation of Solvency II will lead to a better understanding of risk, increasing the resilience and competitiveness of insurance companies. Firms see this, and more insurers are no longer passively reacting to the changes brought about by Solvency II. Increasingly, firms see the changes as an opportunity to proactively implement measures that improve exposure data quality and exposure data management. As a result, many reinsurers apply significant surcharges to cedants that are perceived to have low-quality exposure data and exposure management standards. Conversely, reinsurers are more likely to provide premium credits of 5 to 10 percent or offer additional capacity to cedants that submit high-quality exposure data.
Rating agencies and investors also expect more stringent exposure management processes and higher exposure data standards. Sound exposure data practices are, therefore, increasingly a priority for senior management, and changes are driven with the mindset of benefiting from the competitive advantage that high-quality exposure data offers. To fight the decrease of data quality, insurers spend considerable time and resources to re-format and re-enter exposure data as its being passed on along the insurance chain and between departments within each individual touch point on the chain.
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However, due to the different systems, data standards and contract definitions in place a lot of this work remains manual and repetitive, inviting human error. This month we have the 25th anniversary of the most damaging cluster of European windstorms on record—Daria, Herta, Wiebke, and Vivan.
This cluster of storms highlighted the need for better understanding the potential impact of clustering for insurance industry. However, since then we have not seen such a clustering again of such significance, so how important is this phenomena really over the long term? There has been plenty of discourse over what makes a cluster of storms significant, the definition of clustering and how clustering should be modeled in recent years.
Today the industry accepts the need to consider the impact of clustering on the risk, and assess its importance when making decisions on underwriting and capital management. However, identifying and modeling a simple process to describe cyclone clustering is still proving to be a challenge for the modeling community due to the complexity and variety of mechanisms that govern fronts and cyclones.
But the insurance industry is mostly concerned with severity of the storms. Thus, how do we define a severe cluster? Are we talking about severe storms, such as those in and , which had very extended and strong wind footprints. There are actually multiple descriptions of storm clustering, in terms of storm severity or spatial hazard variability.
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While backtesting is one of the main tools for the validation of an internal model, it is not the only one but should be complementary to other techniques such as stress testing and reverse stress testing , scenario analysis, etc. Furthermore, the rules state that backtesting of internal models should be performed at least once a year. A key element when validating a model is described in the below section; this is backtesting. When a company uses an internal model that should be evaluated using backtesting , which under Solvency II can be defined as a tool for the validation process in quantitative terms of an internal model to analyze if it is appropriate, and compares the resulting risk estimates with past experience.
This technique should be complementary to others, in order to verify the correct alignment of the internal model to determine capital charges under the new framework. Backtesting is a statistical procedure used to validate a model by comparing actual results empirical distribution of gains and losses and the risk measures generated by the models.
Internal models calculate capital charges for the various risks like the standard model by using the VaR Value at Risk approach. Formally, VaR is the loss level such that there is a probability that losses are equal to or greater than :.
Please confirm the following
Backtesting consists of analyzing the failures that the model has in relation to the level of failures that it should have. Therefore, a basic element of backtesting is the number of times the actual losses exceed the VaR in a given period. Where is the estimated loss for the time by using the information available in , is the loss observed in and is the indicator of the event of an exception, exceeded, failure or failed in.
There are multiple different backtesting tests, and they can be grouped into large families, which can be implemented for model validation and will be discussed in the next section. There is no exclusive test against which to measure the validity of a VaR model, as in backtesting the models various desired properties can be measured. Therefore we can group different proposed tests into the following testing families:. These tests focus exclusively on checking whether the estimated VaR is exceeded at a rate above the confidence level with which it was estimated The probability of a loss exceeding the VaR occurring must then be 0.
If losses occur at a higher rate, assuming that we have a large enough sample, the calculated VaR underestimates the portfolio risk.
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Otherwise, i. Unconditional tests only take the number of exceptions into account, but not how they are distributed over time. Failed values should occur independently from each other, but bad models tend to produce sequences of consecutive exceeded values. The analysis of the independence can be done through implementing various tests that focus on checking whether there is any relationship between the failed values. Test sets examine the properties of independence and unconditional coverage while making it possible to identify models that have shortcomings for failing either of the two properties.
Solvency II and backtesting internal models
While these tests may seem more appropriate, since both properties are evaluated simultaneously, they have the limitation of being least able to detect VaR measurements that only fail to fulfill one of the two properties. The above tests only analyze the adequacy of the VaR for a given confidence level. However, an accurate measurement of the VaR should be valid for any confidence level.
This type of test assumes that if the calculation of the VaR is adequate, a In addition, the failed values presented within a given level should also be independent of those presented at other confidence levels. Instead of focusing solely on the number of exceeded values, like the previous tests, we could consider their amount or magnitude.
In this respect, if we have two models with the same number of independent failed values, intuition tells us to choose the one in which the magnitude of the exceeded value is lower. As if the losses of a model are too large, this may be the result of the wrong model being used. There are several statistical tests in the specialized literature that consider the magnitude of the excess values when validating a model. Besides the above tests based on counting the number of exceptions at one or several confidence levels, their dependence or study of their size can be done by complementary analysis, such as analyzing the relationship between the VaR estimated by the model and the distribution of actual gains and losses, studies to identify the causes of exceptions, etc.
We will now focus on the analysis of the relationship between returns and the estimated VaR, which is an aspect related to the efficiency of the VaR measurement. An appropriate risk measurement must not only be conservative enough, i.
In this regard, it would be advisable for large VaR figures to be accompanied by large negative returns, while small VaR calculations must be associated with small negative returns or positive yields. Various tests may be used to verify whether this relationship is strong. In this section we will show a simple application of a major backtesting test used in specialized literature to validate a model, by employing the case of equity risk. To do this, we analyzed the trend of monthly logarithmic returns of the FTSE over an extended period of time observations , by using an approach based on the normal distribution model.
The backtesting conducted in this example will be made within the sample or in simple, which will make it possible to calculate the estimation of the risk made by the model at each time point with historical losses. Under the null hypothesis, if the model is correct, POF it is distributed as a x 2 with a degree of leeway, so that if the value of the statistic exceeds the critical value, the null hypothesis is rejected and the model is considered as inadequate.
For a significance level of 5 percent the null hypothesis is rejected because the value of the statistic 4, exceeds the critical value 3. Internal models may be used by insurance companies to calculate the required capital requirements in Solvency II. To ensure that the models used are appropriate, the rules stipulate the requirement for a process to be put in place to validate them.
Backtesting is a quantitative tool to check whether the resulting estimates of the model are in line with past experience. There are other tools that are required to complete the analysis, such as scenario analysis, stress tests, reverse stress tests, etc. Studying different backtesting techniques shows that there is no exclusive test against which to directly measure the validity of a VaR model. Since tests analyze different properties that failed values of a model should comply with, large families have been established addressing these complementary aspects of a series of failed values of a model to ensure that an insurance company uses an appropriate model.