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.

本文提出了一种建立与市场数据一致的期限结构的方法，并提供平均波动性随着期限增加而降低的利率。该方法专为连续重复使用而设计，与 Diebold 和 Li 的工作一致，提供合理的外推率，并随着时间的推移具有适当的波动水平。采用Svensson模型，通过遗传算法和拟牛顿非线性优化方法相结合来估计其参数。我们创新了一个新的目标函数，该函数专注于估计曲线的两个部分（内插和外推）。为此，添加了稳定性成分。新的目标函数旨在解决估计市场上不可观察的长期利率的问题，其估计值通常是人为稳定或过度波动的。结果表明，该估计方法能够使外推利率的波动性达到与最长流动利率观察到的水平一致的水平。估计误差足够小，并且没有统计证据表明它们存在偏差。该方法对于保险市场很有用，因为它提供的利率不会导致人为稳定或过度波动的技术条款。