Speaker(s): Sergey Smirnov, Andrey Zanochkin, Marat Kurbangaleev, Victor Lapshin (Financial Engineering and Risk Management Lab)
The EIOPA approach for constructing the risk-free yield curve is based on the Smith-Wilson method (SW); its weaknesses due to the nature of the extrapolation problem, data quality and the choice of the fitting method, have been actively discussed over the last years. First, it is stressed in the literature that, being an exact fitting method, SW is extremely sensitive to small changes in the market data (swap rates), especially for the extrapolated rates at the longest maturities. EIOPA enhanced the robustness of curve estimate by discarding a part of the data, eliminating some of the tenors from 10 to 20 years.
However, the sensitivity to noise-like changes in the data remains significant and is usually higher than that to parallel shifts. Second, SW can produce negative discount factors; EIOPA deems to avoid negativity by restricting certain "relaxation" parameter, but recent literature provides a case of this drawback. We propose a consistent modification to the EIOPA methodology ensuring robustness, allowing to use more complete data (including tenors excluded by EIOPA), while remaining tractable and replicable. First, we modify the problem setting: instead of exact fitting we use approximate one.
The higher is the approximation precision , the less is the curve smoothness; this can be controlled by an adequate choice of the regularization parameter, related to possible current price fluctuations as measured by typical bid-ask spreads. Second, we slightly change the mathematical formulation to prevent the occurrence of negative discount factors, while preserving the framework in general. Applied to historical data, the proposed modification produces the results comparable to the original EIOPA methodology in terms of the value and volatility for the liabilities typical for life insurance companies or pension funds. Therefore it is not burdening market participants while being more robust and therefore less subject to errors and manipulations.