On the volatility of the yield curve of the Colombian public debt market
Main Article Content
Keywords
temporary structure of interest rates, volatility, autoregressive vectors, principal components, causality
Abstract
This paper estimates the volatility of the Temporary Structure of Interest Rates (ETTI) of the Colombian public debt market and explains its relationship with macroeconomics fundamentals. Starting from the parametric model proposed by Nelson and Siegel (1987), the ETTI is estimated in order to capture the conditional volatility component with the Autoregressive Conditional Heteroskedasticity models (ARCH). Subsequently the relationship with the macroeconomic variables such as the gross domestic product ( ), the general price level ( ), the monetary policy interest rate ( ) and the risk country ( ) is evaluated through impulse-response function of the Structural Vector Autoregressive models (SVAR) and the Granger causality tests. The results show that the volatility of the ETTI of the Colombian public debt market has asymmetric effects and there are causal relationships in both directions with some of the macroeconomic variables. However, when there are shocks among them, there are only significant unidirectional responses from macroeconomics to ETTI volatility and not in the opposite direction.
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References
Alexander, C. (2000). Orthogonal Methods for Generating Large Positive Semi-Definite Covariance Matri-ces.
Discussion Papers in Finance 2000-06, ICMA Centre, The University of Reading. Recuperado de http://www.academia.edu/29534484/Orthogonal_Methods_for_Generating_Large_Positive_Semi-Definite_Covariance_Matrices
________. (2001a). A
Primer on the Orthogonal GARCH Model. Recuperado de http://carolalexander.org/publish/download/DiscussionPapers/OrthogonalGARCH_Primer.pdf
________. (2001b). Principal Component Models for Generating Large GARCH Covariance Matrices. Recuperado de http://www.carolalexander.org/publish/download/JournalArticles/PDFs/Economic%20 Notes_31_2_337-359.pdf
Alexander, C., & Chibumba, A. (1997). Multivariate Orthogonal Factor GARCH. Working paper, University of Sussex Discussion Papers in Mathematics.
Ang, A., & Piazzesi, M. (2003). A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables. Journal of Monetary Economics, 50, 745-787. doi:10.1016/S03043932(03)00032-1
Arango, L., González, A., León, J., & Melo, L. (2006). Cambios en la tasa de intervención y su efecto en la estructura a plazo de Colombia. Borradores de Economía, 424. Recuperado de http://www.banrep.gov.co/es/borrador-424
Bautista, R., Riascos, Á., & Suárez, N. (marzo, 2007). La aplicación de un modelo de factores a las curvas de rendimiento del mercado de deuda pública colombiano. Recuperado de https://administracion.uniandes.edu.co//images/stories/pdf/06020014_Galeras.pdf
Bernanke, B., & Blinder, A. (1992). The Federal Funds Rate and the Channels of Monetary Transmission. The American Economic Review, 82(4), 901-921. Recuperado de http://links.jstor.org/sici?sici=0002-8282%28199209%2982%3A4%3C901%3ATFFRAT%3E2.0.CO%3B2-1&origin=repec
Black, F., Derman, E., & Toy, W. (1990). A One-Factor Model Of Interest Rates And Its Application To Treasury Bond Options. Financial Analyst Journal, 46(1), 33-39. Recuperado de https://pdfs.semanticscholar.org/6ecb/f463899fdf6a71e272a13153899e3da7ff88.pdf
Bliss, R. (1997). Movements in the Term Structure of Interest Rates.
Federal Reserve Bank of Atlanta. Economic Review, 82(4), 16-33. Recuperado de https://www.frbatlanta.org/-/media/documents/research/publications/economic-review/1997/vol82no4_bliss.pdf
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity.
Journal of Econometrics, 31, 307-327. Recuperado de https://doi.org/10.1016/0304-4076(86)90063-1
Botero, J., & Ramírez, A. (2007). La volatilidad de la tasa de interés a corto plazo: un ejercicio para la economía colombiana, 2001-2006. Revista Ingenierías Universidad de Medellín, 6(11), 149-170. Recuperado de http://www.scielo.org.co/pdf/rium/v6n11/v6n11a10.pdf
Brennan, M., & Schwartz, E. (1979). A continuos time approach to pricing.
Journal of Banking & Finance, 3(2), 133-155. Recuperado de https://doi.org/10.1016/0378-4266(79)90011-6
Chacón, R. (2004). Construcción de La Curva Cupón Cero. Caso Colombiano. Trabajo presentado en I Simposio de Docentes de Finanzas. Recuperado de https://core.ac.uk/download/pdf/7074843.pdf
Chirinos, A., & Bolívar, M. (2012).
Volatility term structure and estimation of yield curve: Inferring their connections and movements. Recuperado de http://www.cemla.org/red/papers2006/2012-red-xvii-54.pdf
Cox, J., Ingersoll, J., & Ross, S. (1985). A Theory of the Term Structure of Interest Rate. Econometrica, 53(2), 385-407. Recuperado de http://www.jstor.org/stable/1911242
Cuadros, C. (2015). Descomposición de la estructura a términos de las tasas de interés de los bonos soberanos de Estados Unidos y Colombia. Revista de Economía del Rosario, 18(02), 309-342. Recuperado de http://dx.doi.org/10.12804/rev.econ.rosario.18.02.2015.05
De Goeij, P., & Marquering, W. (2006). Macroeconomic announcements and asymmetricvolatility in bond returns. Journal of Banking & Finance, 30(10), 2659-2680.
Díaz, A., Jareño, F., & Navarro, E. (2009). Estimating the Volatility Term Structure. En M. Corazza & C. Pizzi (eds.). Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 123-131). Milano: Springer Verlag. doi: 10.1007/978-88-470-1481-7_13
________. (2010). Term Structure of Volatilities and Yield Curve Estimation Methodology. Quantitative Finance, 11, 573-568. doi: 10.1080/14697680903473286
Diebold, F., & Li, C. (2006). Forecasting the Term Structure of Government Bond Yields. Journal of Econometrics, 130(2), 337-364. Recuperado de https://doi.org/10.1016/j.jeconom.2005.03.005
Diebold, F., Rudebusch, G., & Aruoba, B. (2006). The macroeconomy and the yield curve: A dynamic latent factor approach. Journal of Econometrics, 131(1-2), 309-338. Recuperado de https://doi.org/10.1016/j.jeconom.2005.01.011
Elton, E., Gruber, M., & Michaely, R. (1990). The Structure of Spot Rates and Immunization. The Journal of Finance, 45(2), 629-643. doi: 10.2307/2328675
Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom. Econometrica, 50(4), 987-1007. doi: 10.2307/1912773
Estrella, A., & Hardouvelis, G. (1991). The Term Structure as a Predictor of Real Economic Activity. The Journal of Finance, 46(2), 555-576. doi: 10.2307/2328836
Evans, C., & Marshall, D. (1998). Monetary policy and the term sctructure of nominal interest rates: Evidence and theory. Carnegie-Rochester Conference Series on Public Policy, 49, 53-111.
________. (2001). Economic Determinants of the Nominal Treasury Yield Curve. Recuperado de http://www.chicagofed.org/digital_assets/publicati ... s/2001/Wp2001-16.pdf
Fernández, H. (2009). EGARCH: un modelo asimétrico para estimar la volatilidad de las series financieras. Revista Ingenierías Universidad de Medellín, 9(16), 49-60. Recuperado de http://revistas.udem.edu.co/index.php/ingenierias/article/view/240
Ferrer, R., González, C., & Soto, G. (2008). Key Factors in the Term Structure of Volatility of Interest Rates. Trabajo presentado en XI Encuentro de Economía Aplicada. Recuperado de http://encuentros.alde.es/anteriores/xieea/trabajos/pdf/126.pdf
Fong, H. G., & Vasicek, O. (1991). Interest Rate Volatility as a Stochastic Factor.
Working Paper, Gifford Fong Associates.
Haldane, A., & Read, V. (1999). Monetary Policy and Yield Curve. Bank of England. Quarterly Bulletin, 39(2), 171-176.
________. (2000). Monetary Policy Surprises and the Yield Curve. Bank of England, Working Paper Series, 106. Recuperado de http://www.ssrn.com/abstract=228869
Hardouvelis, G. (1994). The Term Structure and Future Changes in the Long and Short Rates in the G7 Countries. Journal of Monetary Economics, 33(2), 255-283. doi: 10.1016/0304-3932(94)90003-5
Heidari, M., & Wu, L. (2003). Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates? The Journal of Fixed Income, 13, 75-86. Recuperado de http://faculty.baruch.cuny.edu/lwu/papers/span_jfi2003.pdf
Ho, T., & Lee, S-B. (1986). Term Structure Movements and Pricing Interest Rate Contingent Claims. The Journal of Finance, 41(5), 1011-1029. doi: 10.2307/2328161
Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417.
Hull, J., & White, A. (1987). The Pricing of Options on Assets with Stochastic Volatilities. The Journal of Finance, 42(2), 281-300. doi: 10.2307/2328253
________. (1990). Pricing Interest-Rate-Derivatives Securities. The Review of Financial Studies, 3(4), 573-592.
Jareño, F., & Tolentino, M. (2012). The US volatility term structure: A principal component analysis. African Journal of Business Management, 6(2), 615-626. doi: 10.5897/AJBM11.2100
Joslin, S., & Konchitchki, Y. (2017). Interest Rate Volatility, the Yield Curve, and the Macroeconomy. Journal of Financial Economics, 128(2), 207-402. doi: 10.1016/j.jfineco.2017.12.004
Lekkos, I. (2000). A Critique of Factor Analysis of Interest Rates. The Journal of Derivatives, 8(1), 72-83. doi: 10.3905/jod.2000.319111
Litterman, R., & Scheinkman, J. (1991). Common Factors Affecting Bond Returns.
The Journal of Fixed Income, 1(1), 54-61. doi: 10.3905/jfi.1991.692347
Longstaff, F., & Schwartz, E. (1992). Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model. The Journal of Finance, 47(4), 1259-1282. Recuperado de http://www.anderson.ucla.edu/faculty/eduardo.schwartz/articles/45.pdf
Matzner-løber, E., & Villa, C. (2004).
Functional Principal Component Analysis of the Yield Curve. Recuperado de https://www.researchgate.net/publication/255660098_Functional_Principal_Component_Analysis_of_the_Yield_Curve
Mayorga, W. (2007). The Yield Curve and Macroeconomics Factors in Emerging Economics: The Colombian Case (tesis de maestría). Universidad de York, Department of Economics and Related Studies, MSc Finance and Econometrics, United Kingdom.
McCallum, B. (2005). Monetary Policy and the Term Structure of Interest Rates.
Federal Reserve Bank of Richmond Economic Quarterly, 91(4), 1-21. Recuperado de http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.6186&rep=rep1&type=pdf
Melo, L., & Becerra, O. (2006). Una aproximación a la dinámica de las tasas de interés de corto plazo en Colombia a través de modelos GARCH multivariados.
Borradores de Economía, 366. Recuperado de
http://www.banrep.gov.co/sites/default/files/publicaciones/pdfs/borra366.pdf
Melo, L., & Castro, G. (2010). Relación entre variables macro y la curva de rendimientos. Borradores de Economía, 605. Recuperado de http://www.banrep.gov.co/sites/default/files/publicaciones/pdfs/borra605.pdf
Nelson, C., & Siegel, A. (1987). Parsimonious Modeling of Yield Curves.
The Journal of Business, 60(4), 473-489. Recuperado de http://cepr.org/sites/default/files/events/1854_NS_1987.pdf
Nelson, D. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach.
Econometrica, 59(2), 347-370. doi: 10.2307/2938260
Novales, A., & Benito, S. (2005). A factor analysis of volatility across the term structure: the Spanish case. Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE), 2. Recuperado de http://eprints.ucm.es/7872/
Pearson, K. (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.
Périgon, C., & Villa, C. (2006). Sources of Time Variation in the Covariance Matrix of Interest Rates. The Journal of Business, 79(3), 1235-1549. doi: 10.1086/500684
Sims, C. (1986). Are Forecasting Models Usable for Policy Analysis?
Federal Reserve Bank of Minneapolis Quarterly Review, 10(1), 2-17. Recuperado de https://www.minneapolisfed.org/research/qr/qr1011.pdf
Soto, G. (2004). Using Principal Component Analysis to Explain Term Structure Movements Performance and Stability. En A. Tavidzem (ed.), Progress in Economics Research, 8. Nueva York: Nova Science Publishers.
Strickland, C. (1993). Interest Rate Volatility and the Term Structure of Interest Rates. Recuperado de
https://www2.warwick.ac.uk/fac/soc/wbs/subjects/finance/research/wpaperseries/1993/93-37.pdf
Svensson, L. (1994). Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994. Working Paper 4871. National Bureau of Economic Research, Massachusetts. Recuperado de http://www.nber.org/papers/w4871.pdf
Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure.
Journal of Financial Economics, 5(2), 177-188. doi: 10.1016/0304-405X(77)90016-2
Vasicek, O., & Fong, H. G. (1982). Term Structure Modeling Using Exponential Splines. The Journal of Finance, 37(2), 339-348. doi: 10.2307/2327333
Wu, T. (octubre, 2003). What Makes the Yield Curve Move. Risks and Rewards Newsletter, 43, 24-26.
Discussion Papers in Finance 2000-06, ICMA Centre, The University of Reading. Recuperado de http://www.academia.edu/29534484/Orthogonal_Methods_for_Generating_Large_Positive_Semi-Definite_Covariance_Matrices
________. (2001a). A
Primer on the Orthogonal GARCH Model. Recuperado de http://carolalexander.org/publish/download/DiscussionPapers/OrthogonalGARCH_Primer.pdf
________. (2001b). Principal Component Models for Generating Large GARCH Covariance Matrices. Recuperado de http://www.carolalexander.org/publish/download/JournalArticles/PDFs/Economic%20 Notes_31_2_337-359.pdf
Alexander, C., & Chibumba, A. (1997). Multivariate Orthogonal Factor GARCH. Working paper, University of Sussex Discussion Papers in Mathematics.
Ang, A., & Piazzesi, M. (2003). A No-Arbitrage Vector Autoregression of Term Structure Dynamics with Macroeconomic and Latent Variables. Journal of Monetary Economics, 50, 745-787. doi:10.1016/S03043932(03)00032-1
Arango, L., González, A., León, J., & Melo, L. (2006). Cambios en la tasa de intervención y su efecto en la estructura a plazo de Colombia. Borradores de Economía, 424. Recuperado de http://www.banrep.gov.co/es/borrador-424
Bautista, R., Riascos, Á., & Suárez, N. (marzo, 2007). La aplicación de un modelo de factores a las curvas de rendimiento del mercado de deuda pública colombiano. Recuperado de https://administracion.uniandes.edu.co//images/stories/pdf/06020014_Galeras.pdf
Bernanke, B., & Blinder, A. (1992). The Federal Funds Rate and the Channels of Monetary Transmission. The American Economic Review, 82(4), 901-921. Recuperado de http://links.jstor.org/sici?sici=0002-8282%28199209%2982%3A4%3C901%3ATFFRAT%3E2.0.CO%3B2-1&origin=repec
Black, F., Derman, E., & Toy, W. (1990). A One-Factor Model Of Interest Rates And Its Application To Treasury Bond Options. Financial Analyst Journal, 46(1), 33-39. Recuperado de https://pdfs.semanticscholar.org/6ecb/f463899fdf6a71e272a13153899e3da7ff88.pdf
Bliss, R. (1997). Movements in the Term Structure of Interest Rates.
Federal Reserve Bank of Atlanta. Economic Review, 82(4), 16-33. Recuperado de https://www.frbatlanta.org/-/media/documents/research/publications/economic-review/1997/vol82no4_bliss.pdf
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity.
Journal of Econometrics, 31, 307-327. Recuperado de https://doi.org/10.1016/0304-4076(86)90063-1
Botero, J., & Ramírez, A. (2007). La volatilidad de la tasa de interés a corto plazo: un ejercicio para la economía colombiana, 2001-2006. Revista Ingenierías Universidad de Medellín, 6(11), 149-170. Recuperado de http://www.scielo.org.co/pdf/rium/v6n11/v6n11a10.pdf
Brennan, M., & Schwartz, E. (1979). A continuos time approach to pricing.
Journal of Banking & Finance, 3(2), 133-155. Recuperado de https://doi.org/10.1016/0378-4266(79)90011-6
Chacón, R. (2004). Construcción de La Curva Cupón Cero. Caso Colombiano. Trabajo presentado en I Simposio de Docentes de Finanzas. Recuperado de https://core.ac.uk/download/pdf/7074843.pdf
Chirinos, A., & Bolívar, M. (2012).
Volatility term structure and estimation of yield curve: Inferring their connections and movements. Recuperado de http://www.cemla.org/red/papers2006/2012-red-xvii-54.pdf
Cox, J., Ingersoll, J., & Ross, S. (1985). A Theory of the Term Structure of Interest Rate. Econometrica, 53(2), 385-407. Recuperado de http://www.jstor.org/stable/1911242
Cuadros, C. (2015). Descomposición de la estructura a términos de las tasas de interés de los bonos soberanos de Estados Unidos y Colombia. Revista de Economía del Rosario, 18(02), 309-342. Recuperado de http://dx.doi.org/10.12804/rev.econ.rosario.18.02.2015.05
De Goeij, P., & Marquering, W. (2006). Macroeconomic announcements and asymmetricvolatility in bond returns. Journal of Banking & Finance, 30(10), 2659-2680.
Díaz, A., Jareño, F., & Navarro, E. (2009). Estimating the Volatility Term Structure. En M. Corazza & C. Pizzi (eds.). Mathematical and Statistical Methods for Actuarial Sciences and Finance (pp. 123-131). Milano: Springer Verlag. doi: 10.1007/978-88-470-1481-7_13
________. (2010). Term Structure of Volatilities and Yield Curve Estimation Methodology. Quantitative Finance, 11, 573-568. doi: 10.1080/14697680903473286
Diebold, F., & Li, C. (2006). Forecasting the Term Structure of Government Bond Yields. Journal of Econometrics, 130(2), 337-364. Recuperado de https://doi.org/10.1016/j.jeconom.2005.03.005
Diebold, F., Rudebusch, G., & Aruoba, B. (2006). The macroeconomy and the yield curve: A dynamic latent factor approach. Journal of Econometrics, 131(1-2), 309-338. Recuperado de https://doi.org/10.1016/j.jeconom.2005.01.011
Elton, E., Gruber, M., & Michaely, R. (1990). The Structure of Spot Rates and Immunization. The Journal of Finance, 45(2), 629-643. doi: 10.2307/2328675
Engle, R. (1982). Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom. Econometrica, 50(4), 987-1007. doi: 10.2307/1912773
Estrella, A., & Hardouvelis, G. (1991). The Term Structure as a Predictor of Real Economic Activity. The Journal of Finance, 46(2), 555-576. doi: 10.2307/2328836
Evans, C., & Marshall, D. (1998). Monetary policy and the term sctructure of nominal interest rates: Evidence and theory. Carnegie-Rochester Conference Series on Public Policy, 49, 53-111.
________. (2001). Economic Determinants of the Nominal Treasury Yield Curve. Recuperado de http://www.chicagofed.org/digital_assets/publicati ... s/2001/Wp2001-16.pdf
Fernández, H. (2009). EGARCH: un modelo asimétrico para estimar la volatilidad de las series financieras. Revista Ingenierías Universidad de Medellín, 9(16), 49-60. Recuperado de http://revistas.udem.edu.co/index.php/ingenierias/article/view/240
Ferrer, R., González, C., & Soto, G. (2008). Key Factors in the Term Structure of Volatility of Interest Rates. Trabajo presentado en XI Encuentro de Economía Aplicada. Recuperado de http://encuentros.alde.es/anteriores/xieea/trabajos/pdf/126.pdf
Fong, H. G., & Vasicek, O. (1991). Interest Rate Volatility as a Stochastic Factor.
Working Paper, Gifford Fong Associates.
Haldane, A., & Read, V. (1999). Monetary Policy and Yield Curve. Bank of England. Quarterly Bulletin, 39(2), 171-176.
________. (2000). Monetary Policy Surprises and the Yield Curve. Bank of England, Working Paper Series, 106. Recuperado de http://www.ssrn.com/abstract=228869
Hardouvelis, G. (1994). The Term Structure and Future Changes in the Long and Short Rates in the G7 Countries. Journal of Monetary Economics, 33(2), 255-283. doi: 10.1016/0304-3932(94)90003-5
Heidari, M., & Wu, L. (2003). Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates? The Journal of Fixed Income, 13, 75-86. Recuperado de http://faculty.baruch.cuny.edu/lwu/papers/span_jfi2003.pdf
Ho, T., & Lee, S-B. (1986). Term Structure Movements and Pricing Interest Rate Contingent Claims. The Journal of Finance, 41(5), 1011-1029. doi: 10.2307/2328161
Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components. Journal of educational psychology, 24(6), 417.
Hull, J., & White, A. (1987). The Pricing of Options on Assets with Stochastic Volatilities. The Journal of Finance, 42(2), 281-300. doi: 10.2307/2328253
________. (1990). Pricing Interest-Rate-Derivatives Securities. The Review of Financial Studies, 3(4), 573-592.
Jareño, F., & Tolentino, M. (2012). The US volatility term structure: A principal component analysis. African Journal of Business Management, 6(2), 615-626. doi: 10.5897/AJBM11.2100
Joslin, S., & Konchitchki, Y. (2017). Interest Rate Volatility, the Yield Curve, and the Macroeconomy. Journal of Financial Economics, 128(2), 207-402. doi: 10.1016/j.jfineco.2017.12.004
Lekkos, I. (2000). A Critique of Factor Analysis of Interest Rates. The Journal of Derivatives, 8(1), 72-83. doi: 10.3905/jod.2000.319111
Litterman, R., & Scheinkman, J. (1991). Common Factors Affecting Bond Returns.
The Journal of Fixed Income, 1(1), 54-61. doi: 10.3905/jfi.1991.692347
Longstaff, F., & Schwartz, E. (1992). Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model. The Journal of Finance, 47(4), 1259-1282. Recuperado de http://www.anderson.ucla.edu/faculty/eduardo.schwartz/articles/45.pdf
Matzner-løber, E., & Villa, C. (2004).
Functional Principal Component Analysis of the Yield Curve. Recuperado de https://www.researchgate.net/publication/255660098_Functional_Principal_Component_Analysis_of_the_Yield_Curve
Mayorga, W. (2007). The Yield Curve and Macroeconomics Factors in Emerging Economics: The Colombian Case (tesis de maestría). Universidad de York, Department of Economics and Related Studies, MSc Finance and Econometrics, United Kingdom.
McCallum, B. (2005). Monetary Policy and the Term Structure of Interest Rates.
Federal Reserve Bank of Richmond Economic Quarterly, 91(4), 1-21. Recuperado de http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475.6186&rep=rep1&type=pdf
Melo, L., & Becerra, O. (2006). Una aproximación a la dinámica de las tasas de interés de corto plazo en Colombia a través de modelos GARCH multivariados.
Borradores de Economía, 366. Recuperado de
http://www.banrep.gov.co/sites/default/files/publicaciones/pdfs/borra366.pdf
Melo, L., & Castro, G. (2010). Relación entre variables macro y la curva de rendimientos. Borradores de Economía, 605. Recuperado de http://www.banrep.gov.co/sites/default/files/publicaciones/pdfs/borra605.pdf
Nelson, C., & Siegel, A. (1987). Parsimonious Modeling of Yield Curves.
The Journal of Business, 60(4), 473-489. Recuperado de http://cepr.org/sites/default/files/events/1854_NS_1987.pdf
Nelson, D. (1991). Conditional Heteroskedasticity in Asset Returns: A New Approach.
Econometrica, 59(2), 347-370. doi: 10.2307/2938260
Novales, A., & Benito, S. (2005). A factor analysis of volatility across the term structure: the Spanish case. Documentos de trabajo del Instituto Complutense de Análisis Económico (ICAE), 2. Recuperado de http://eprints.ucm.es/7872/
Pearson, K. (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.
Périgon, C., & Villa, C. (2006). Sources of Time Variation in the Covariance Matrix of Interest Rates. The Journal of Business, 79(3), 1235-1549. doi: 10.1086/500684
Sims, C. (1986). Are Forecasting Models Usable for Policy Analysis?
Federal Reserve Bank of Minneapolis Quarterly Review, 10(1), 2-17. Recuperado de https://www.minneapolisfed.org/research/qr/qr1011.pdf
Soto, G. (2004). Using Principal Component Analysis to Explain Term Structure Movements Performance and Stability. En A. Tavidzem (ed.), Progress in Economics Research, 8. Nueva York: Nova Science Publishers.
Strickland, C. (1993). Interest Rate Volatility and the Term Structure of Interest Rates. Recuperado de
https://www2.warwick.ac.uk/fac/soc/wbs/subjects/finance/research/wpaperseries/1993/93-37.pdf
Svensson, L. (1994). Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994. Working Paper 4871. National Bureau of Economic Research, Massachusetts. Recuperado de http://www.nber.org/papers/w4871.pdf
Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure.
Journal of Financial Economics, 5(2), 177-188. doi: 10.1016/0304-405X(77)90016-2
Vasicek, O., & Fong, H. G. (1982). Term Structure Modeling Using Exponential Splines. The Journal of Finance, 37(2), 339-348. doi: 10.2307/2327333
Wu, T. (octubre, 2003). What Makes the Yield Curve Move. Risks and Rewards Newsletter, 43, 24-26.