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Model validation Wtp interest risk – Pension fund sector

Estimated reading time: 6 minutes

In this article we will perform a qualitative model validation on the Wtp interest rate risk model. This model is used for pension funds in The Netherlands. The pension fund sector in Europe does not have an overarching European regulation yet. This means that every country has its own regulation and its own risk models. For example, the Netherlands introduced new national pension fund regulation (Wtp – Wet toekomst pensioenen) in July 2023.

Wtp simulation sets provided by the DNB

The Wtp interest risk models are based on scenario-sets provided by the Dutch Central Bank (DNB – De Nederlandsche Bank). These scenario’s contain projections 100 years into the future. These are based on the model1, assumptions and parameters as published by the Commissie Parameters 2022.

For the transfer of pension capital from a defined benefits (DB) pension to a new (Wtp) pension fund one has to use the ‘risk-neutral’ Q simulation set. After that a ‘economic’ P simulation set must be used to calculate and report the 5% and 95% VaR scenario’s to the pension clients. This P simulation contains a risk-premium based on market information and on ECB and CPB (Centraal Planbureau) inflation objectives. 

DNB has published these simulation-sets since the start of 2023. Therefore it is not yet possible to make statements about the historical performance of these models.

However, we still can say something about their usefulness. We do this by calculating the risk on the 10 year maturity risk-free interest rate using the Wtp models. We then compare them to theSolvency II standard formula model and to market expectations as obtained from the forward curve.

Wtp Q simulation

First we compare the new risk-neutral Wtp Q model with the Solvency II Standard model (revised 2020 version):

Figure 1. Solvency II vs Wtp Q simulation. The graph above compares the Wtp Qinterest rate risk projections for the 95% (red), 50% (black) and 5% scenario (green) against the ‘extended Solvency II standard formula’ model (dashed red/green).We also include the market expectation as derived from the forwards on a 10 year maturity zero-bond (dashed black). Source data: Dutch National Bank as of end of June 2023. Calculations and graph: Asset Mechanics.

For a one-year ahead projection, we observe that the Wtp Q model is slightly more conservative than the Solvency II standard formula model. It should be noted that Wtp Q makes projections multiple years into the future. SII only provides one-year ahead projections. We therefore compare Wtp Q with an ‘extended’ Solvency II standard formula model and scale it using IID normality assumption. Of course, this assumption does not fully hold. But comparing such an extended model to Wtp Q helps us to make statements about the underlying process and distribution of Wtp Q. For a 10-years maturity interest rate Wtp Q has a wider risk range than the extended Solvency II standard formula. This shows us that Wtp Q draws from a distribution with a higher standard deviation. The relative widening of Wtp between year 2 and year 10 also indicates that more autocorrelation between subsequent years is available. 

When we generate this graph for short maturities we see the opposite effect. We then note that the Wtp Q risk range is much narrower than the extended Solvency II projection. This shows us that for short maturities Wtp Q currently obtains a lower risk profile than the extended Solvency II model.

We also can compare the expected Wtp Q rate (VaR 50% scenario) with the forward curve. We then see that the long term forward expectation is almost 2% lower than the expected value from Wtp Q.

Among drivers that bring interest rates down, we often find aging population and lower productivity. Fiscal stimulus policies would act in the opposite direction. Research suggests that for many countries the effects of the downward pressures have been larger than the upward pressures. See also:IMF blog article about historical drivers of natural rates. These drivers might explain why the market expects a lower long-term interest rate than what we experienced historically. And also why it would be lower than the risk neutral Wtp Q model expectation.

Wtp P simulation

Figure 2. Wtp Q vs Wtp P simulation. The graph above compares the Wtp P interest rate risk projections for the 95% (dark red), 50% (black) and 5% scenario (dark green) with the Wtp Q model (light red/green). We include the market expectation as derived from the forwards on a 10 year maturity zero-bond for comparison (dashed black). Source data: Dutch Central Bank as of end of June 2023. Calculations and graph: Asset Mechanics.

When we look at the Wtp P model we see that the 50% scenario tracks the forward curve pretty well after year 5. This indeed seems to suggest that the expected value of Wtp P is much more in line with the market than Wtp Q. 

However, for the first 5 years it does not align at all with the market expectation from the forward curve. Wtp P projects that the interest rate would be 2% lower than the market expectation based on the 10-year forward for June 2024. It appears that the model parameters are selected assuming quick reversion to ECB inflation objectives.

The upper and lower risk percentiles of Wtp P show a relatively narrow range around the 50% scenario.

We note that both the expectation as the risk range around Wtp P are quite different from Wtp Q. They also differ from historical risk profiles which we explore in the next article about the BASE model. According to the model description by the commission that set the requirements for the Wtp models, this difference can be attributed torisk aversion, as people are willing to pay a risk-premium to obtain a certain future cash-flow2.


Overall, we can make a few observations from this qualitative model validation of the Wtp interest risk. We noted quite some differences between statistical reality, market expectations and central bank objectives.

The Wtp Q model provides wider risk estimations than an extended Solvency II model. In the previous article we noted thatSolvency II did not always perform that well in the last 20 years. This would imply that Wtp Q would be more appropriate to capture the risks. However, we also noted that Wtp Q does not align well with the long term market expectations.

The Wtp P risk model is designed to be an economic model. We note that it aligns with market expectations from the forward-curve, especially for the long-term forwards. For the short-term horizon we note that it does not follow market expectations, but rather the central bank’s objectives.

In addition, we note quite narrow risk estimates for Wtp P. It is important to understand these narrow bands within the statistical reality of ever changing macro-economic conditions. According to Wtp model descriptions this would be related to the risk premium that people would be willing to pay to obtain a more certain future cashflow stream.

How do other models perform? Let’s explore a pure data-driven statistical method –the BASE modeland a model that adapts to changing regimes in the following articles.


  1. CP2022 model ↩︎
  2. appendix report advise commission (2022/11/29)page 53 box 4.1. The risk-premium would be paid to cover for long interest, inflation and macro long life risks in the far future. ↩︎