El proceso estocástico de Feller y el modelo Cox-Ingersoll-Ross: modelación de tasas de interés y valoración de bonos
Feller Stochastic process and Cox-Ingersoll-Ross model: Interest rate modeling and bond valuation
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León Nieto, D.I. 2017. El proceso estocástico de Feller y el modelo Cox-Ingersoll-Ross: modelación de tasas de interés y valoración de bonos. ODEON. 13 (may 2017), 31–44. DOI:https://doi.org/10.18601/17941113.n13.03.
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Este artículo presenta el modelo Cox-Ingersoll-Ross para la modelación de tasas de interés y su relación con el proceso estocástico de Feller; como un modelo paramétrico se muestran las principales sensibilidades a sus parámetros y sus aplicaciones.
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Referencias (VER)
Andersen Torben G. Lund, J. (1997). Estimating continous-time stochastic volatility models of the short-term interest rate. Journal of Econometrics, 77, 343-377.
Black, F. y Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47(4), 52-59.
Black, F., Derman, E. y Toy, W. (1990). A one-factor model of interest rates and its application to Treasury bond options. Financial Analysts Journal, 46, 33-39.
Brown, R. H. Schaefer, S. M (1994). The term structure of real interest rates and the Cox, Ingersoll and Ross Model. Journal of Financial Economics, 35, 3-42.
Cox, J. C., Ingersoll Jr, J. E. y Ross, S. A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53 (2), 385-407.
Dothan L. (1978). On the term structure of interest rates. Journal of Financial Economics, 6, 59-69.
Feller, W. (1951a). Two singular diffusion problems. Annals of Math, 54 (1), 173-182.
Feller, W. (1951b). Diffusion processes in genetics. En Neyman, J. (ed.). Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability (pp. 227-246). Berkeley: University of California Press.
Ho, T. y Lee, S. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41 (5), 1129-1142.
Hull, J. y White, A. (1990). Pricing Interest Rate Derivative Securities. Review of Financial Studies, 3 (4), 573-592.
Kouritzin, M. A. y Rémillard, B. (2002). Explicit strong solutions of multidimensional stochastic differential equations. Technical report, Laboratory for Research in Probability and Statistics. University of Ottawa-Carleton University.
Lepage, T., Law, S., Tupper, P. y Bryant, D. (2006). Continuous and tractable models for the variation of evolutionary rates. Recuperado de http://arxiv.org/abs/math.pr/0506145.
Lamberton, D. y Lapeyre, B. (2008). Introduction to Stochastic Calculus Applied to Finance (2 edition). Boca Raton, FL: Chapman & Hall/CRC Financial Mathematics Series.
Milstein, G. N. (1975). Approximate Integration of Stochastic Differential Equations. Theory of Probability & Its Applications, 19 (3), 557-000.
Pedersen, A.R. (2000). Estimating the nitrous oxide emission rate from the soil surface by means of a diffusion model. Scandinavian Journal of Statistics, 27, 385-403.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177-188.
Black, F. y Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47(4), 52-59.
Black, F., Derman, E. y Toy, W. (1990). A one-factor model of interest rates and its application to Treasury bond options. Financial Analysts Journal, 46, 33-39.
Brown, R. H. Schaefer, S. M (1994). The term structure of real interest rates and the Cox, Ingersoll and Ross Model. Journal of Financial Economics, 35, 3-42.
Cox, J. C., Ingersoll Jr, J. E. y Ross, S. A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53 (2), 385-407.
Dothan L. (1978). On the term structure of interest rates. Journal of Financial Economics, 6, 59-69.
Feller, W. (1951a). Two singular diffusion problems. Annals of Math, 54 (1), 173-182.
Feller, W. (1951b). Diffusion processes in genetics. En Neyman, J. (ed.). Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability (pp. 227-246). Berkeley: University of California Press.
Ho, T. y Lee, S. (1986). Term structure movements and pricing interest rate contingent claims. Journal of Finance, 41 (5), 1129-1142.
Hull, J. y White, A. (1990). Pricing Interest Rate Derivative Securities. Review of Financial Studies, 3 (4), 573-592.
Kouritzin, M. A. y Rémillard, B. (2002). Explicit strong solutions of multidimensional stochastic differential equations. Technical report, Laboratory for Research in Probability and Statistics. University of Ottawa-Carleton University.
Lepage, T., Law, S., Tupper, P. y Bryant, D. (2006). Continuous and tractable models for the variation of evolutionary rates. Recuperado de http://arxiv.org/abs/math.pr/0506145.
Lamberton, D. y Lapeyre, B. (2008). Introduction to Stochastic Calculus Applied to Finance (2 edition). Boca Raton, FL: Chapman & Hall/CRC Financial Mathematics Series.
Milstein, G. N. (1975). Approximate Integration of Stochastic Differential Equations. Theory of Probability & Its Applications, 19 (3), 557-000.
Pedersen, A.R. (2000). Estimating the nitrous oxide emission rate from the soil surface by means of a diffusion model. Scandinavian Journal of Statistics, 27, 385-403.
Vasicek, O. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177-188.
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