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15 Aug 2012, Ross Evans , Neal Hegeman , Insurance Risk

An ultimate forward rate (UFR)-based extrapolation of the euro risk-free rate curve now seems very much on the cards for Solvency II, but is also being introduced for Danish pension funds and Dutch insurers ahead of the formal adoption of Solvency II. This has profound implications for the swap hedges required to stabilise solvency, as well as having knock-on impacts for the euro swap market.

**Solvency II**

All of the parties negotiating Solvency II – the European Commission, European Parliament and European Council – have included a variation of the UFR-based extrapolation in their proposal for Solvency II. Under each proposal, the euro risk-free rate curve is based on the market swap curve up to 20 years, but extrapolated thereafter. The extrapolation is calibrated so that the forward rates converge to a level of 4.2% (the UFR) after 10 years (Parliament) or 40 years (Commission and Council). These proposals result in a risk-free rate curve that sits significantly higher than the market swap curve beyond 20 years onwards, as illustrated in figure 1.

**Implications for hedging long-dated liabilities**

The extrapolation of the Solvency II curve beyond 20 years leads to a significant reduction in the volume and tenor of swaps needed to hedge liabilities past this point. The size of this reduction is driven, to a large extent, by the value of ‘alpha’ – the parameter used to control the speed at which the extrapolation converges to the UFR.

Alpha is closely related to the level of the forward rate immediately before the 20-year cut-off point, as well as the required speed of convergence. In particular, the further away the forwards are from 4.2% at the 20-year point, the bigger alpha needs to be.

Figure 2 shows the relationship between the one-year rate in 19 years’ time (19f 1y) and the value of alpha. It also shows what this means for the modified duration of a 50-year bullet liability. As the 19f 1y rate moves away from 4.2%, alpha has to be increased from its default value of 0.1. This causes the duration of the liability to fall, reaching 22 years when alpha has a value of 0.45 (as would be required for current low forward rates).

**Concluding remarks**

Hedging the Solvency II risk-free rate is not straightforward, due to the dependence of duration on forward rates. For insurers, there is also the added complication of managing the trade-off between capital stability and capital minimisation, which may require non-linear solutions.

The current proposals should drive a steepening of the euro swap curve between 20 and 50 years, as pension funds and insurers look to shorten their euro swap hedges.

The Insurance ALM Advisory team at RBS has carried out extensive research on optimal hedge strategies for hedging the Solvency II risk-free rate.