Estimated reading time: 7 minutes

In this article we perform a model validation on Solvency II interest rate risk standard formula.

## Solvency II and insurance companies

The insurance sector in Europe is governed by Solvency II regulation. It prescribes quarterly reporting of 1-year ahead Value at Risk 99.5% confidence levels. These are considered conservative 1-in-200 years scenarios and are used for the determination of capital requirements. An important component of the Solvency II interest rate risk calculation is the standard formula provided by EIOPA.

The interest rate risk model is implemented on both the assets and liabilities of insurance companies. It is applied on all interest related investments as well as on future client obligations. The interest risks on these two cashflow streams are ideally similar in size and have opposing signs. Big discrepancies could have substantial impact on the viability of insurance companies. Therefore, the calculation of interest rate risk is not a negligible task.

In 2020 EIOPA performed a model review on the standard formula. This led to some adjustments to the model. The sector will have to implement these changes after acceptance by the European Commission.

Hereby we review the performance of the interest rate risk based on the **standard formula** **2016** and the updated **2020** version.

## Validation of Solvency II standard formula interest rate risk – 2016 version

In order to review the Solvency II standard formula (2016 version), we perform a backtest over the last 20 years. For every month, starting from August 2004, we compare the one-year ahead risk projection against the respective realised interest rate. The results are displayed in Figure 1.

#### Breaches of the lower range

Our first observation from the graph is that the realised interest rates move roughly within the projected upper and lower range. When looking at the projected lower risk range, we would expect 0.5% breaches according to the model specification. However, in reality we observe that the realised rates breach the lower limit in 25% of the month-year combinations during the observation period . The majority of breaches occurred in 2015, 2016 and 2019-2021 due to decreasing interest rates.

This implies that the model did not capture the low interest rate dynamics well in The Netherlands. The number of breaches was far over the accuracy quality standards as specified by BIS and BASEL^{1}. This was also one of the reasons for EIOPA to adjust the interest risk model in the 2020 model update.

#### Breaches of the upper range

With regards to the projected upper limit, we observe breaches in 8% of the months (relative to expectation of 0.5% based on model specification). The main contributor for that is the 2022 period. This period was characterised by strong inflationary pressure and imbalances in demand and supply after the Covid-19 pandemic and political instability. It shows that Solvency II model was not able to adapt enough to rapid changes in the macro-economic environment.

## Validation of Solvency II standard formula interest rate risk – 2020 update

We proceed with backtesting of the proposed model update (2020 version) and estimate how it would have performed over the same validation period of 20 years. The results are displayed in Figure 2.

From the graph above, it is apparent that the 2020 version indeed corrects the issues with the downside movements. Those are now more aligned with the projected range. The results indicate 1% realised breaches vs an expectation of 0.5%. This is a significant improvement from the 25% value in Figure 1.

Nevertheless, this model does not fully capture the swift interest rate increases in 2022. In fact, we observe that 6% of the realised interest rates are beyond the upper limit during our test period while we expect 0.5%. Overall, it seems that both versions of the Solvency II standard formula are not adaptive enough to capture rapidly changing macro-economic environments.

#### Model validation since 1950

For completeness, we have extended the validation period and performed a backtest on the updated Solvency II SF model (2020 version) from 1950 until February 2024. We have done so by using yearly interest rate data before 2004 and monthly data since 2004. The results are displayed in Figure 3 below.

Over this longer validation period we note that the accuracy improves substantially. On the upper side, 2% breaches are observed relative to the expected 0.5%. However, the average costs^{2} over this period were very high at around 5.3% for the upper percentile. We can observe that the model is too strict in the higher interest rate period 1950-2005, while simultaneously not strict enough in the low interest rate period following since 2015.

This shows that the current model calibration settings would not work properly in other economic environments. And that future recalibrations will be needed to ensure effectiveness if conditions change.

## Other models

How do other regulatory models perform? Let’s take a look at the new Wtp interest rate risk models for the pension fund sector in The Netherlands. Further, we perform a review of a pure data-driven statistical method –the BASE model. And we evaluate and compare multiple models to select the optimal model for decision making.

Interested to learn how the Solvency II interest rate risk standard formula could be applied in practise? Feel free to exploreour interest rate risk calculator.

#### Footnotes

- Basel Committee on Banking Supervision 2016. Minimal capital requirements for market risk. With 250 observations up to 5 exceptions (2%) are considered acceptable (green), 5-10 exceptions (2-4%) raise questions (yellow) and over 10 exceptions (>4%) almost certainly indicate a problem with the model (red). ↩︎
- For the definition ofaverage model costsee the article on optimal risk model selection ↩︎