Abstract
<p>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.</p>
Highlights
According to Bingham (2013), working with financial series involves a series of challenges since financial series tend to show asymmetry, i.e., bias, leptokurtosis, and periods of high volatility resulting from the complex financial and economic environment
The purpose of this paper is to develop a methodology for the estimation of the volatility of the fixed-income markets in Mexico that includes the analysis of zero-coupon bonds, fixed rate bonds, inflation-linked bonds and interest rate swaps
The results obtained using the principal components analysis suggest, as mentioned in several studies, that only the first three components are enough to explain more than 80% of the variance for the different yield curves
Summary
According to Bingham (2013), working with financial series involves a series of challenges since financial series tend to show asymmetry, i.e., bias, leptokurtosis, and periods of high volatility resulting from the complex financial and economic environment. Fixed-income instruments trade in yield, which allows investors to know and compare the return of different assets independently of the maturity or size of the coupon. The variance of this yield could be estimated using the percentage change or a simple difference change. It was decided to use a GARCH(1,1) because this model tends to be a standard With these estimations, and using the orthogonality of the variable, it is possible to obtain the square root to obtain the volatility of the yield curve or even that of all the fixed-income market.
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