Extrapolating Long-Run Yield Curves: An Innovative and Consistent Approach

Abstract

This article proposes a method to build term structures that are consistent with market data and that provide interest rates for which the volatility, on average, decreases as maturities increase. The method is designed for continuous repetitive use and is consistent with work by Diebold and Li, providing reasonable extrapolated rates, with an appropriate level of volatility over time. The Svensson model is adopted, and its parameters are estimated by the combination of a genetic algorithm and a quasi-Newton nonlinear optimization method. We innovate with a new objective function that focuses on both parts of the estimated curves (interpolated and extrapolated). For this purpose, a stability component is added. The new objective function aims to solve the problem of estimating long-term rates not observable in the market, for which the estimates are usually artificially stable or excessively volatile. The results show that the estimation method is able to bring the volatility of extrapolated rates to levels consistent with those observed for the longest liquid rate. Estimation errors are small enough and there is no statistical evidence that they are biased. The method is useful for the insurance market, since it provides interest rates that do not lead to artificially stable or excessively volatile technical provisions.

ACKNOWLEDGMENTS

The authors thank any anonymous referee for the useful comments that helped to improve the article.

FUNDING

Thiago Signorelli and César Neves thank SUSEP for the support in carrying out this research.

Carlos Heitor Campani thanks the following Brazilian institutions for financial support to his research: Brasilprev Research Chair, ENS (Escola de Negócios e Seguros), CNPq (National Council for Scientific and Technological Development), FAPERJ (Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro), and Quantum Finance (Data Provider).

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