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Model validation Solvency II interest risk – Insurance sector

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

The insurance sector in Europe is governed by Solvency II regulations. The Solvency II standard formula risk models, which are used by the majority of the insurance companies, are provided by EIOPA and are effective as of 2016. A model review was performed in 2020 and is to be implemented by the sector after acceptance by the European Commission. The Solvency II regulation prescribes the use of Value at Risk 99.5% confidence levels which is considered a conservative 1 in 200 year scenario.

For interest rate risk the model is applied both on interest related investments as well as on future client obligations. Therefore it’s calculation is not a negligible task. Hereby we are going to review the performance of 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

Let’s first review the current Solvency II standard formula (2016 version) by running a backtest over the last 20 years to validate how it performed. For every month starting from August 2004 we compare the one-year ahead risk projection against the respective realised interest rate:  

Solvency II standard formula Interest risk model performance validation (2016 model version)
Figure 1. Validation of Solvency II standard formula interest rate risk model performance (2016 model version). The graph shows the realised risk-free interest rate on a 10 year maturity zero-coupon bond as provided by DNB (black). The dashed lines (red: 99.5% and green: 0.5%) show the one-year ahead risk projections as calculated by the original Solvency II standard formula – 2016 version. The grey dashed line shows the market expectation as given by the one-year forward on a 10 year maturity zero-bond. In addition the following metrics are provided: correlation of 85% between the realized interest rate and the one-year forward expectation; validation for VaR99.5 indicates that 93% of observations fall below the 99.5 percentile; for VaR0.5 we see that 24% of the observations fall below the 0.5th percentile.

Our first observation from the graph is that the realised interest rates move roughly within the projected upper and lower range. However, when looking more closely we note that the market expectation as given by the forward is not always a good predictor, especially in times of market stress. And secondly, when looking at the projected lower risk range, we note that while we would expect 0,5% of breaches according to the model specification, we in reality observe that the lower limit has been breached in 24% of the months of our observation period. Most of those 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. This was also one of the reasons for EIOPA to adjust the interest risk model in the 2020 model update. 

With regards to interest rate increases we see that the upper limit has been breached in 7% of the months of the observation period where we would expect 0.5%. The main contributor for that is the 2022 period, characterised by fast rising inflation and imbalances in demand and supply after the Covid-19 pandemic and political instability. This means that the rapid changes in the macro-economic environment were also not captured well by the Solvency II model.

Let’s now review the proposed model update (2020 version) and see how it would have performed over the same validation period of almost 20 years: 

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

Solvency II standard formula Interest risk model performance validation (2020 version)
Figure 2. Validation of Solvency II standard formula interest rate risk model performance (2020 model version). The graph shows the realised risk-free interest rate on a 10 year maturity zero-coupon bond as provided by DNB (black). The dashed lines (red: 99.5% and green: 0.5%) show the one-year ahead risk projections as calculated by the updated Solvency II standard formula – 2020 version. The grey dashed line shows the market expectation as given by the one-year forward on a 10 year maturity zero-bond.

From the graph above we see that the proposed new Solvency II standard formula interest model (2020 version) indeed corrects the issues with the downside movements. These now fall much more within the projected range. We now see just 1% breaches while 0.5% is to be expected.

However, also this model does not fully capture the swift interest rate increases in 2022. In fact, we observe that 6% of the realised interest rates fall over the upper limit during our test period while 0.5% is to be expected. Overall it seems that both 2016 and the 2020 updated version of the Solvency II standard formula are not adaptive enough to capture the rapidly changing macro-economic environments.

How do other regulatory models perform? Let’s take a closer look at somenew interest rate risk models for the pension fund sector in the Netherlands in the following article.

If you want to learn how the 2020 version of the Solvency II standard formula can be used to calculate the risks on a loan portfolio, please also try out our interest rate risk calculator.

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