An econometric approach for the estimation of the Mexican yield curves volatility index

Resumen

In this paper a methodology is proposed to measure volatility in Mexican yield curves, including the nominal, real, and swap rates. To obtain the volatility, the GARCH model was used to estimate the volatilities of the first three main principal components of each yield curve. The GARCHs obtained of the first three orthogonal components are modelling the volatility of the parallel shift, the slope changes (twist), and the changes in curvature (butterfly). To obtain the volatility index, it is necessary to use the variances obtained using the orthogonality of the series added and then obtain the square root of the sum. This approach also allows the estimation of defined semi-positive variance-covariance matrices for the different nodes of the curve that can be used in portfolio optimization or in the computation of risk measures. The data for the analysis correspond to the market information from October 2015 to November 2017.