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Model validation Wtp interest risk – Pension fund sector

In this article we will perform a qualitative model validation on the Wtp interest rate risk model 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 the Netherlands a new national pension fund regulation (Wtp – Wet toekomst pensioenen) was introduced in July 2023.

The interest risk models under this regulation are based on scenario-sets that are provided by the Dutch Central Bank (DNB – De Nederlandsche Bank) with projections 100 years into the future. These scenario-sets are based on the assumptions and parameters as published by the Commissie Parameters 2022.

For the transfer of pension capital from an old (FTK) pension fund to a new (Wtp) pension fund the so-called ‘risk-neutral’ Q simulation set is to be used. 

After transition a so-called ‘market-consistent’ P simulation set is to be used to report 5% and 95% VaR scenario’s to pension clients. This P simulation contains a risk-premium that is based both on market information and on ECB and CPB (Centraal Planbureau) inflation objectives. 

As these simulation-sets have only been published since the start of 2023, it is not yet possible to make statements about the historical performance of these models.

However, we can say something about the usefulness of these models. We do this by calculating the risk on the 10 year risk-free interest rate using the Wtp models, comparing it 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 interest rate risk projections for the 95% (red), 50% (black) and 5% scenario (green) as provided by the Wtp Q simulation set against the ‘extended Solvency II standard formula’ model (dashed red/green). Also the market expectation as derived from the forwards on a 10 year maturity zero-bond is included for comparison (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. As Wtp Q makes projections multiple years into the future while SII only gives us a one-year ahead projection we compare Wtp Q with an ‘extended’ Solvency II standard formula model which is scaled 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 the distribution of Wtp Q is drawn from a distribution with a higher standard deviation and/or that more autocorrelation between subsequent years is available. For short maturities on the other hand we see that the Wtp Q risk range is much narrower than the extended Solvency II projection. This shows us that there is much more mean reversion present for the short term maturities under Wtp Q.

When we compare the expected Wtp Q rate (VaR 50% scenario) with the forward curve we see that the current long term market expectation as given by the forward curve is almost 2% lower than the expected value from Wtp Q.

Aging population and lower productivity are often cited as drivers that bring interest rates down, while 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:IMF blog article about historical drivers of natural rates). These drivers might indicate why the market expects a lower long-term interest rate than what we have historically experienced and what would be obtained by the risk neutral Wtp Q model.

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). Also the market expectation as derived from the forwards on a 10 year maturity zero-bond is included 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, which indeed seems to suggest that Wtp P is much more ‘market-consistent’ 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. Given the historical reality of a variety of macro-economic scenario’s over the last century (see also next article on BASE and REGIME-BASED models) we wonder how much forward looking value this range of value has and how realistic it is to show this narrow range on longer horizons.


Overall, we can conclude from this brief model validation of the Wtp interest risk that, at least for the 10 year maturity interest rate, there are 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. As we noted in the previous article thatSolvency II did not always perform that well in the last 20 years, this might indicate that Wtp Q would be more appropriate to capture the risks. However, we also note that Wtp Q does not align well with the long term market expectations.

The Wtp P risk model, which is meant to be more market consistent, does indeed align much more 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 that it seems to be driven by central bank’s objectives. As we do not have enough history on the output from this model, it is still early to say if this approach would yield better results over a longer period.

In addition, we note quite narrow risk estimates. It is important to understand these narrow bands within the statistical reality of ever changing macro-economic conditions. In our validation of the Solvency II model we saw that these changes happen quite fast, therefore it is to be expected that future estimations of Wtp P can be totally different. If we would use this model therefore to make (investment) decisions, it would be best to have an adaptive approach and do so shortly after every quarterly update.

Can other models also help us to make better decisions? Let’s explore some statistical models that adapt to changing regimes in the following articles.