<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0186-1042</journal-id>
<journal-title><![CDATA[Contaduría y administración]]></journal-title>
<abbrev-journal-title><![CDATA[Contad. Adm]]></abbrev-journal-title>
<issn>0186-1042</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Facultad de Contaduría y Administración]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0186-10422020000300012</article-id>
<article-id pub-id-type="doi">10.22201/fca.24488410e.2020.2377</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[An econometric approach for the estimation of the Mexican yield curves volatility index]]></article-title>
<article-title xml:lang="es"><![CDATA[Un enfoque econométrico para la estimación del índice de volatilidad de las curvas de tasas en México]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Álvarez del Castillo Penna]]></surname>
<given-names><![CDATA[Raúl]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Núñez Mora]]></surname>
<given-names><![CDATA[José Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Mota Aragón]]></surname>
<given-names><![CDATA[Martha Beatriz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Tecnológico y de Estudios Superiores de Monterrey  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Autónoma Metropolitana  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>09</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>09</month>
<year>2020</year>
</pub-date>
<volume>65</volume>
<numero>3</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0186-10422020000300012&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0186-10422020000300012&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0186-10422020000300012&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract 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></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En este artículo se propone medir la volatilidad de las curvas de tasas nominal, real y swap en México. Para obtener la volatilidad, se usó el modelo GARCH para estimar las volatilidades de las tres primeras componentes principales de cada curva. Los GARCH&#8217;s obtenidos de las tres primeras componentes ortogonales modelan la volatilidad de los cambios paralelo, en pendiente y en curvatura. Para obtener el índice de volatilidad es necesario usar las varianzas obtenidas usando la ortogonalidad de las series agregadas y entonces la raíz cuadrada de la suma. Este enfoque permite la estimación de las matrices de varianzas y covarianzas semipositivas definidas para los diferentes nodos, que pueden ser usadas para la optimización de los portafolios o en el cálculo de medidas de riesgo. Los datos corresponden al periodo de octubre del 2015 a noviembre del 2017.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Interest rates]]></kwd>
<kwd lng="en"><![CDATA[Principal components]]></kwd>
<kwd lng="en"><![CDATA[Orthogonal GARCH]]></kwd>
<kwd lng="en"><![CDATA[Yield curve]]></kwd>
<kwd lng="en"><![CDATA[Variance-covariance matrix]]></kwd>
<kwd lng="en"><![CDATA[G12]]></kwd>
<kwd lng="en"><![CDATA[G15]]></kwd>
<kwd lng="es"><![CDATA[Tasas de interés]]></kwd>
<kwd lng="es"><![CDATA[Componentes principales]]></kwd>
<kwd lng="es"><![CDATA[GARCH Ortogonal]]></kwd>
<kwd lng="es"><![CDATA[Curva de rendimiento]]></kwd>
<kwd lng="es"><![CDATA[Matriz de varianza-covarianza]]></kwd>
<kwd lng="es"><![CDATA[G12]]></kwd>
<kwd lng="es"><![CDATA[G15]]></kwd>
</kwd-group>
</article-meta>
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