Medición del valor en riesgo de portafolios de renta fija usando modelos multifactoriales dinámicos de tasas de interés
DOI:
https://doi.org/10.1016/j.estger.2017.02.003Palabras clave:
Tasas de interés, Modelos dinámicos, Valor en riesgo, Portafolios de renta fijaResumen
En este trabajo se evalúa el desempeno de tres modelos dinámicos de la estructura a plazos de tasas ˜ de interés para estimar el valor en riesgo (VaR, por su traducción de Value at Risk) de portafolios de renta fija. De esta forma, se encuentra que el modelo de Diebold, Rudebusch y Aruoba se desempena˜ adecuadamente respecto a las pruebas de backtesting del VaR, mientras que el modelo de Diebold y Li y un modelo afín de no arbitraje exhiben un pobre desempeno. Los tres modelos asumen que la matriz de ˜ varianzas y covarianzas de los factores latentes a cada modelo es constante, lo cual limita su utilidad en el cálculo del VaR. Por lo tanto, modelos que relajen este supuesto deberían ofrecer un mejor desempeno˜ y ser más adecuados para la gestión del riesgo de portafolios de renta fija.Descargas
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Referencias
Abad, P. y Benito, S. (2007). Value at risk in fixed income portfolios: A comparison between empirical models of the term structure. The Business Review Cambridge, 7(2), 342.
Abad, P., Benito, S. y López, C. (2014). A comprehensive review of Value at Risk methodologies. The Spanish Review of Financial Economics, 12(1), 15–32.
Aït-Sahalia, Y. (2008). Closed-form likelihood expansions for multivariate diffusions. The Annals of Statistics, 36(2), 906–937.
Aït-Sahalia, Y. y Kimmel, R. L. (2010). Estimating affine multifactor term structure models using closed-form likelihood expansions. Journal of Financial Economics, 98(1), 113–144.
Arango, L. F., Melo, L. y Vásquez, D. M. (2001). Estimación de la estructura a plazo de las tasas de interés en Colombia (Borradores de Economía No. 210). Bogotá, Colombia: Banco de la República de Colombia.
Beltratti, A. y Colla, P. (2007). A portfolio-based evaluation of affine term structure models. Annals of Operations Research, 151(1), 193–222.
Berkowitz, J. y O'Brien, J. (2002). How accurate are value-at-risk models at commercial banks? The Journal of Finance, 57(3), 1093–1111.
Brandt, M. y Chapman, D. (2003). Comparing multifactor models of the term structure. Working paper. Duke University [consultado 10 Dic 2015]. Disponible en: https://faculty.fuqua.duke.edu/mbrandt/papers/working/mfcompare.pdf
Caldeira, J. F., Moura, G. V. y Santos, A. A. (2015). Measuring risk in fixed income portfolios using yield curve models. Computational Economics, 46(1), 65–82.
Castro, G. A. y Melo, L. (2010). Relación entre variables macro y la curva de rendimientos (Borradores de Economía No. 605). Bogotá, Colombia: Banco de la República de Colombia.
Christensen, J. H., Diebold, F. X. y Rudebusch, G. D. (2009). An arbitrage-free generalized Nelson-Siegel term structure model. The Econometrics Journal, 12(3), 33–64.
Christensen, J. H., Diebold, F. X. y Rudebusch, G. D. (2011). The affine arbitrage-free class of Nelson-Siegel term structure models. Journal of Econometrics, 164(1), 4–20.
Christoffersen, P. (1998). Evaluating interval forecasts. International Economic Review, 39(4), 841–862.
Christoffersen, P. y Pelletier, D. (2004). Backtesting value-at-risk: A duration-based approach. Journal of Financial Econometrics, 2(1), 84–108.
Cox, J. C., Ingersoll, J. E., Jr. y Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica, 53(2), 363–384.
Creal, D. D. y Wu, J. C. (2015). Estimation of affine term structure models with spanned or unspanned stochastic volatility. Journal of Econometrics, 185(1), 60–81.
Dai, Q. y Singleton, K. J. (2000). Specification analysis of affine term structure models. The Journal of Finance, 55(5), 1943–1978.
Date, P. y Bustreo, R. (2015). Value-at-Risk for fixed-income portfolios: A Kalman filtering approach. IMA Journal of Management Mathematics, 27(4), 557–573.
De Pooter, M. (2007). Examining the Nelson-Siegel class of term structure models (Tinbergen Institute Discussion Papers). Amsterdam, Holanda: Tinbergen Institute.
Diebold, F. X. y Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics, 130(2), 337–364.
Diebold, F. X., Rudebusch, G. y Aruoba, B. (2006). The macroeconomy and the yield curve: A dynamic latent factor approach. Journal of Econometrics, 131(1), 309–338.
Diebold, F. X. y Rudebusch, G. D. (2011). The Dynamic Nelson-Siegel Approach to Yield Curve Modeling and Forecasting. Princeton, NJ: Princeton University Press.
Diebold, F. X. y Rudebusch, G. D. (2013). Yield Curve Modeling and Forecasting. Princeton, NJ: Princeton University Press.
Duffee, G. R. (2002). Term premia and interest rate forecasts in affine models. The Journal of Finance, 57(1), 405–443.
Duffee, G. (2013). Bond Pricing and the Macroeconomy. En G. M. Constantinides, H. Milton, y R. M. Stulz (Eds.), Handbook of the Economics of Finance (Volume 2) (pp. 907–967). Elsevier. Part B.
Duffie, D. y Kan, R. (1996). A yield-factor model of interest rates. Mathematical Finance, 6(4), 379–406.
Ferreira, M. (2005). Forecasting the comovements of spot interest rates. Journal of International Money and Finance, 24(5), 766–792.
Ferreira, M. y Lopez, J. (2005). Evaluating interest rate covariance models within a value-at-risk framework. Journal of Financial Econometrics, 3(1), 126–168.
Gomez-Restrepo, J. y Restrepo-Tobón, D. A. (2016). Estimating the Colombian yield curve using a dynamic model with macrofactors (Working Paper). Medellín, Colombia: Universidad EAFIT [consultado 10 Feb 2016]. Disponible en: http://hdl.handle.net/10784/9553.
Gürkaynak, R. S. y Wright, J. H. (2012). Macroeconomics and the term structure. Journal of Economic Literature, 50(2), 331–367.
Haas, M. (2001). New Methods in Backtesting (Working paper in Financial Engineering). Bonn, Germany: Research Center Caesar [consultado 13 Dic 2015]. Disponible en: https://www.ime.usp.br/rvicente/risco/haas.pdf
Jorion, P. (2006). Value at risk (3 rd ed). New York, NY: McGraw-Hill.
Kim, D. H. y Orphanides, A. (2012). Term structure estimation with survey data on interest rate forecasts. Journal of Financial and Quantitative Analysis, 47(1), 241–272.
Kupiec, P. (1995). Techniques for verifying the accuracy of risk management models. Journal of Derivatives, 3(2), 73–84.
Litterman, R. B. y Scheinkman, J. (1991). Common factors affecting bond returns. The Journal of Fixed Income, 1(1), 54–61.
Longerstaey, J. (1996). Mapping to describe positions (Technical Document 4 th ed.). New York: Morgan RiskMetrics.
Lopez, J. A. (1998). Methods for evaluating value-at-risk estimates. FRBNY Economic Policy Review, 4(3), 119–124.
Lopez, J. (1999). Regulatory evaluation of Value-at-Risk models. Journal of Risk, 1(2), 37–63.
Maldonado, R., Pantoja, J. O. y Zapata, N. (2015). Estimación dinámica de una estructura de tasas de interés para Colombia: Análisis empírico de filtros de Kalman. Journal of Economics & Administrative Science, 19(37), 70–77.
Martellini, L. y Meyfredi, J. C. (2007). A copula approach to Value-at-Risk estimation for fixed-income portfolios. Journal of Fixed Income, 17(1), 5–15.
Melo, L. y Granados, J. (2011). Regulación y valor en riesgo. Ensayos sobre Política Económica, 29(64), 110–177.
Nelson, C. R. y Siegel, A. F. (1987). Parsimonious modelling of the yield curves. Journal of Business, 60(4), 473–489.
Pérignon, C. y Smith, D. R. (2007). Yield-factor volatility models. Journal of Banking & Finance, 31(10), 3125–3144.
Piazzesi, M. (2010). Affine term structure models. En Y. Ait-Sahalia y L. P. Hansen (Eds.), Handbook of Financial Econometrics (pp. 691–766). New York: Elsevier.
Rezende, R. B. y Ferreira, M. S. (2011). Modeling and forecasting the yield curve by an extended Nelson-Siegel class of models: A quantile autoregression approach. Journal of Forecasting, 30(8), 339–350.
Santos, A. A., Nogales, F. J., Ruiz, E. y van Dijk, D. (2012). Optimal portfolios with minimum capital requirements. Journal of Banking & Finance, 36(7), 1928–1942.
Sousa, J. B., Esquıvel, M. L., Gaspar, R. M. y Real, P. C. (2012). Bonds historical simulation value at risk (Working paper). Lisboa, Portugal: Universidade NOVA de Lisboa [consultado 10 Ene 2016]. Disponible en: http://www.cma.fct.unl.pt/sites/www.cma.fct.unl.pt/files/documentos/publicacoes/pdf 2012/CMA%2032012.pdf
Su, E. y Knowles, T. W. (2010). Measuring bond portfolio Value at Risk and expected shortfall in US Treasury market. Asia Pacific Management Review, 15(4), 477–501.
Svensson, L. O. (1994). Estimating and interpreting forward interest rates: Sweden 1992-1994 (IMF Working Papers 94/114). Washington DC: International Monetary Fund [consultado 11 Ene 2016]. Disponible en: http://ideas.repec.org/p/imf/imfwpa/94-114.html
Trolle, A. B. y Schwartz, E. S. (2009). A general stochastic volatility model for the pricing of interest rate derivatives. Review of Financial Studies, 22(5), 2007–2057.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.
Velásquez-Giraldo, M. y Restrepo-Tobón, D. A. (2016). Affine term structure models: Forecasting the yield curve for Colombia. Lecturas de Economía, 85, 53–90.
Vlaar, P. J. (2000). Value at risk models for Dutch bond portfolios. Journal of Banking & Finance, 24(7), 1131–1154.
Abad, P., Benito, S. y López, C. (2014). A comprehensive review of Value at Risk methodologies. The Spanish Review of Financial Economics, 12(1), 15–32.
Aït-Sahalia, Y. (2008). Closed-form likelihood expansions for multivariate diffusions. The Annals of Statistics, 36(2), 906–937.
Aït-Sahalia, Y. y Kimmel, R. L. (2010). Estimating affine multifactor term structure models using closed-form likelihood expansions. Journal of Financial Economics, 98(1), 113–144.
Arango, L. F., Melo, L. y Vásquez, D. M. (2001). Estimación de la estructura a plazo de las tasas de interés en Colombia (Borradores de Economía No. 210). Bogotá, Colombia: Banco de la República de Colombia.
Beltratti, A. y Colla, P. (2007). A portfolio-based evaluation of affine term structure models. Annals of Operations Research, 151(1), 193–222.
Berkowitz, J. y O'Brien, J. (2002). How accurate are value-at-risk models at commercial banks? The Journal of Finance, 57(3), 1093–1111.
Brandt, M. y Chapman, D. (2003). Comparing multifactor models of the term structure. Working paper. Duke University [consultado 10 Dic 2015]. Disponible en: https://faculty.fuqua.duke.edu/mbrandt/papers/working/mfcompare.pdf
Caldeira, J. F., Moura, G. V. y Santos, A. A. (2015). Measuring risk in fixed income portfolios using yield curve models. Computational Economics, 46(1), 65–82.
Castro, G. A. y Melo, L. (2010). Relación entre variables macro y la curva de rendimientos (Borradores de Economía No. 605). Bogotá, Colombia: Banco de la República de Colombia.
Christensen, J. H., Diebold, F. X. y Rudebusch, G. D. (2009). An arbitrage-free generalized Nelson-Siegel term structure model. The Econometrics Journal, 12(3), 33–64.
Christensen, J. H., Diebold, F. X. y Rudebusch, G. D. (2011). The affine arbitrage-free class of Nelson-Siegel term structure models. Journal of Econometrics, 164(1), 4–20.
Christoffersen, P. (1998). Evaluating interval forecasts. International Economic Review, 39(4), 841–862.
Christoffersen, P. y Pelletier, D. (2004). Backtesting value-at-risk: A duration-based approach. Journal of Financial Econometrics, 2(1), 84–108.
Cox, J. C., Ingersoll, J. E., Jr. y Ross, S. A. (1985). An intertemporal general equilibrium model of asset prices. Econometrica, 53(2), 363–384.
Creal, D. D. y Wu, J. C. (2015). Estimation of affine term structure models with spanned or unspanned stochastic volatility. Journal of Econometrics, 185(1), 60–81.
Dai, Q. y Singleton, K. J. (2000). Specification analysis of affine term structure models. The Journal of Finance, 55(5), 1943–1978.
Date, P. y Bustreo, R. (2015). Value-at-Risk for fixed-income portfolios: A Kalman filtering approach. IMA Journal of Management Mathematics, 27(4), 557–573.
De Pooter, M. (2007). Examining the Nelson-Siegel class of term structure models (Tinbergen Institute Discussion Papers). Amsterdam, Holanda: Tinbergen Institute.
Diebold, F. X. y Li, C. (2006). Forecasting the term structure of government bond yields. Journal of Econometrics, 130(2), 337–364.
Diebold, F. X., Rudebusch, G. y Aruoba, B. (2006). The macroeconomy and the yield curve: A dynamic latent factor approach. Journal of Econometrics, 131(1), 309–338.
Diebold, F. X. y Rudebusch, G. D. (2011). The Dynamic Nelson-Siegel Approach to Yield Curve Modeling and Forecasting. Princeton, NJ: Princeton University Press.
Diebold, F. X. y Rudebusch, G. D. (2013). Yield Curve Modeling and Forecasting. Princeton, NJ: Princeton University Press.
Duffee, G. R. (2002). Term premia and interest rate forecasts in affine models. The Journal of Finance, 57(1), 405–443.
Duffee, G. (2013). Bond Pricing and the Macroeconomy. En G. M. Constantinides, H. Milton, y R. M. Stulz (Eds.), Handbook of the Economics of Finance (Volume 2) (pp. 907–967). Elsevier. Part B.
Duffie, D. y Kan, R. (1996). A yield-factor model of interest rates. Mathematical Finance, 6(4), 379–406.
Ferreira, M. (2005). Forecasting the comovements of spot interest rates. Journal of International Money and Finance, 24(5), 766–792.
Ferreira, M. y Lopez, J. (2005). Evaluating interest rate covariance models within a value-at-risk framework. Journal of Financial Econometrics, 3(1), 126–168.
Gomez-Restrepo, J. y Restrepo-Tobón, D. A. (2016). Estimating the Colombian yield curve using a dynamic model with macrofactors (Working Paper). Medellín, Colombia: Universidad EAFIT [consultado 10 Feb 2016]. Disponible en: http://hdl.handle.net/10784/9553.
Gürkaynak, R. S. y Wright, J. H. (2012). Macroeconomics and the term structure. Journal of Economic Literature, 50(2), 331–367.
Haas, M. (2001). New Methods in Backtesting (Working paper in Financial Engineering). Bonn, Germany: Research Center Caesar [consultado 13 Dic 2015]. Disponible en: https://www.ime.usp.br/rvicente/risco/haas.pdf
Jorion, P. (2006). Value at risk (3 rd ed). New York, NY: McGraw-Hill.
Kim, D. H. y Orphanides, A. (2012). Term structure estimation with survey data on interest rate forecasts. Journal of Financial and Quantitative Analysis, 47(1), 241–272.
Kupiec, P. (1995). Techniques for verifying the accuracy of risk management models. Journal of Derivatives, 3(2), 73–84.
Litterman, R. B. y Scheinkman, J. (1991). Common factors affecting bond returns. The Journal of Fixed Income, 1(1), 54–61.
Longerstaey, J. (1996). Mapping to describe positions (Technical Document 4 th ed.). New York: Morgan RiskMetrics.
Lopez, J. A. (1998). Methods for evaluating value-at-risk estimates. FRBNY Economic Policy Review, 4(3), 119–124.
Lopez, J. (1999). Regulatory evaluation of Value-at-Risk models. Journal of Risk, 1(2), 37–63.
Maldonado, R., Pantoja, J. O. y Zapata, N. (2015). Estimación dinámica de una estructura de tasas de interés para Colombia: Análisis empírico de filtros de Kalman. Journal of Economics & Administrative Science, 19(37), 70–77.
Martellini, L. y Meyfredi, J. C. (2007). A copula approach to Value-at-Risk estimation for fixed-income portfolios. Journal of Fixed Income, 17(1), 5–15.
Melo, L. y Granados, J. (2011). Regulación y valor en riesgo. Ensayos sobre Política Económica, 29(64), 110–177.
Nelson, C. R. y Siegel, A. F. (1987). Parsimonious modelling of the yield curves. Journal of Business, 60(4), 473–489.
Pérignon, C. y Smith, D. R. (2007). Yield-factor volatility models. Journal of Banking & Finance, 31(10), 3125–3144.
Piazzesi, M. (2010). Affine term structure models. En Y. Ait-Sahalia y L. P. Hansen (Eds.), Handbook of Financial Econometrics (pp. 691–766). New York: Elsevier.
Rezende, R. B. y Ferreira, M. S. (2011). Modeling and forecasting the yield curve by an extended Nelson-Siegel class of models: A quantile autoregression approach. Journal of Forecasting, 30(8), 339–350.
Santos, A. A., Nogales, F. J., Ruiz, E. y van Dijk, D. (2012). Optimal portfolios with minimum capital requirements. Journal of Banking & Finance, 36(7), 1928–1942.
Sousa, J. B., Esquıvel, M. L., Gaspar, R. M. y Real, P. C. (2012). Bonds historical simulation value at risk (Working paper). Lisboa, Portugal: Universidade NOVA de Lisboa [consultado 10 Ene 2016]. Disponible en: http://www.cma.fct.unl.pt/sites/www.cma.fct.unl.pt/files/documentos/publicacoes/pdf 2012/CMA%2032012.pdf
Su, E. y Knowles, T. W. (2010). Measuring bond portfolio Value at Risk and expected shortfall in US Treasury market. Asia Pacific Management Review, 15(4), 477–501.
Svensson, L. O. (1994). Estimating and interpreting forward interest rates: Sweden 1992-1994 (IMF Working Papers 94/114). Washington DC: International Monetary Fund [consultado 11 Ene 2016]. Disponible en: http://ideas.repec.org/p/imf/imfwpa/94-114.html
Trolle, A. B. y Schwartz, E. S. (2009). A general stochastic volatility model for the pricing of interest rate derivatives. Review of Financial Studies, 22(5), 2007–2057.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5(2), 177–188.
Velásquez-Giraldo, M. y Restrepo-Tobón, D. A. (2016). Affine term structure models: Forecasting the yield curve for Colombia. Lecturas de Economía, 85, 53–90.
Vlaar, P. J. (2000). Value at risk models for Dutch bond portfolios. Journal of Banking & Finance, 24(7), 1131–1154.
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2017-03-24
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Medición del valor en riesgo de portafolios de renta fija usando modelos multifactoriales dinámicos de tasas de interés. (2017). Estudios Gerenciales, 33(142), 52-63. https://doi.org/10.1016/j.estger.2017.02.003
