Instrumento de cobertura: Heston en MexDer
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nov 17, 2021
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https://doi.org/10.30878/ces.v28n3a9
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Ma. de Lourdes Najera Lopez
http://orcid.org/0000-0002-6824-9561
Raúl de Jesús Gutiérrez
http://orcid.org/0000-0001-6878-3038
http://orcid.org/0000-0002-6824-9561
Raúl de Jesús Gutiérrez
http://orcid.org/0000-0001-6878-3038
Resumen
Se valida el modelo de Heston (1993) para opciones sobre MXN/USD calculando la diferencia que existe entre la prima teórica y la que emite el Mercado Mexicano de Derivados (MexDer). Se estimaron los parámetros en un periodo comprendido de 2003 a 2018 y se calcularon las primas de opciones europeas de compra (call) y venta (put) considerando los precios de ejercicio para el 9 de noviembre de 2018. Los resultados revelan sobrevaloración de opciones call OTM y ITM con una variación de 5.87% y 3.46% respectivamente y para opciones put OTM con un 11.41%, por lo que se ratifica que el modelo es confiable, además se confirma que es un instrumento de cobertura para todos aquellos inversionistas expuestos al riesgo del mercado cambiario.
Article Details
Como citar
NAJERA LOPEZ, Ma. de Lourdes; GUTIÉRREZ, Raúl de Jesús.
Instrumento de cobertura: Heston en MexDer.
CIENCIA ergo-sum, [S.l.], v. 28, n. 3, nov. 2021.
ISSN 2395-8782.
Disponible en: <https://cienciaergosum.uaemex.mx/article/view/14080>. Fecha de acceso: 28 mar. 2025
doi: https://doi.org/10.30878/ces.v28n3a9.
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Ciencias sociales
Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
Citas
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Azencott, R., Gadhyan, Y., & Glowinski, R. (2015). Option pricing accuracy for estimated Heston models. Quantitative Finance, 1-18.
Bates, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in deutsche market options. The Reviews of Financial Studies, 9, 69-107.
Bakshi, C., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of Finance, 52(5), 2003-2049.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654.
Chernov, M., & Ghysels, E. (1998). A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation. Journal of Financial Economics, 56(3), 407-458.
Chesney, M., & Scott, L. (1989). Pricing european currency options: A comparison of the modified blanck-scholes model and a random variance model. Journal of Financial and Quantitative Analysis, 24(3), 267-284.
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Duffie, D., & Singleton, K. (1993). Simulated moments estimation of Markov models of asset prices. Econometrica, 61(4), 929-952.
Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029-1054.
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Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2), 281-300.
Levendorskiĭ, S. (2012). Efficient pricing and reliable calibration in the Heston model. International Journal of Theoretical and Applied Finance, 15(7), 1250050.
Lin, Y. N., Strong, N., & Xu, X. (2001). Pricing FTSE 100 index options under stochastic volatility. The Journal of Futures Markets, 21(3), 197-211.
Liu, J. (1998). Portfolio selection in stochastic environments. The Review of Financial Studies, 20(1), 1-39.
Medina, R. T. y Rodríguez, H. Y. (2010). Una revisión de los modelos de volatilidad estocástica. Comunicaciones en Estadística, 3(1), 79-98. https://doi.org/10.15332/s2027-3355.2010.0001.05
Mondal, M. K., Alim, A., Rahman, F., & Biswas, H. A. (2017). Mathematical analysis of financial model on market price with stochastic volatility. Journal of Mathematical Finance, 7(2), 351-365.
Mykland, P. A., & Zhang, L. (2009). The Econometrics of High Frequency Data. In M. Kessler, A. Lindner, and M. Sorensen (Ed.), Statistical Methods for Stochastic Differential Equations (pp. 109-190). New York: Chapman and Hall/CRC.
Pan, J. (1998). Integrated time-series analysis of spot and option prices. AFA 2001 New Orleans Meetings. https://doi.org/10.2139/ssrn.196808
Roldán, M. L. (2018). Pronóstico de divisas latinoamericanas con modelos de volatilidad estática y estocástica. Ingeniería, 23(2), 166-189.
Schiller, R. (2003, March 22). Risk management for the masses. The Economist.
Scott. L. O. (1987). Option pricing when the variance changes randomly: Theory, estimation, and application. Journal of Financial and Quantitative Analysis, 22, 419-438.
Singh, S., & Dixit, A. (2016). Performance of the Heston’s stochastic volatility model: A study in indian index options market. Theoretical Economics Letters, 6(2), 151-165.
Stiglitz, J. (2002). What I learned at the world economic crisis. The Insider. The New Republic. Robarts Centre for Canadian Studies.
Andersen, T. G., & Sørensen, B. (2010). GMM estimation of a stochastic volatility model: A Monte Carlo study. Journal of Business and Economic Statistics, 14, 328-352.
Azencott, R., Gadhyan, Y., & Glowinski, R. (2015). Option pricing accuracy for estimated Heston models. Quantitative Finance, 1-18.
Bates, D. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in deutsche market options. The Reviews of Financial Studies, 9, 69-107.
Bakshi, C., Cao, C., & Chen, Z. (1997). Empirical performance of alternative option pricing models. The Journal of Finance, 52(5), 2003-2049.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81(3), 637-654.
Chernov, M., & Ghysels, E. (1998). A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation. Journal of Financial Economics, 56(3), 407-458.
Chesney, M., & Scott, L. (1989). Pricing european currency options: A comparison of the modified blanck-scholes model and a random variance model. Journal of Financial and Quantitative Analysis, 24(3), 267-284.
Crisóstomo, R. (2014). An analysis of the Heston stochastic volatility model: Implementation and calibration using Matlab. CNMV Working Paper, 58.
Duffie, D., & Singleton, K. (1993). Simulated moments estimation of Markov models of asset prices. Econometrica, 61(4), 929-952.
Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029-1054.
Heston, S. L. (1993). A closed-form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6(2), 327-343.
Hull, J., & White, A. (1987). The pricing of options on assets with stochastic volatilities. Journal of Finance, 42(2), 281-300.
Levendorskiĭ, S. (2012). Efficient pricing and reliable calibration in the Heston model. International Journal of Theoretical and Applied Finance, 15(7), 1250050.
Lin, Y. N., Strong, N., & Xu, X. (2001). Pricing FTSE 100 index options under stochastic volatility. The Journal of Futures Markets, 21(3), 197-211.
Liu, J. (1998). Portfolio selection in stochastic environments. The Review of Financial Studies, 20(1), 1-39.
Medina, R. T. y Rodríguez, H. Y. (2010). Una revisión de los modelos de volatilidad estocástica. Comunicaciones en Estadística, 3(1), 79-98. https://doi.org/10.15332/s2027-3355.2010.0001.05
Mondal, M. K., Alim, A., Rahman, F., & Biswas, H. A. (2017). Mathematical analysis of financial model on market price with stochastic volatility. Journal of Mathematical Finance, 7(2), 351-365.
Mykland, P. A., & Zhang, L. (2009). The Econometrics of High Frequency Data. In M. Kessler, A. Lindner, and M. Sorensen (Ed.), Statistical Methods for Stochastic Differential Equations (pp. 109-190). New York: Chapman and Hall/CRC.
Pan, J. (1998). Integrated time-series analysis of spot and option prices. AFA 2001 New Orleans Meetings. https://doi.org/10.2139/ssrn.196808
Roldán, M. L. (2018). Pronóstico de divisas latinoamericanas con modelos de volatilidad estática y estocástica. Ingeniería, 23(2), 166-189.
Schiller, R. (2003, March 22). Risk management for the masses. The Economist.
Scott. L. O. (1987). Option pricing when the variance changes randomly: Theory, estimation, and application. Journal of Financial and Quantitative Analysis, 22, 419-438.
Singh, S., & Dixit, A. (2016). Performance of the Heston’s stochastic volatility model: A study in indian index options market. Theoretical Economics Letters, 6(2), 151-165.
Stiglitz, J. (2002). What I learned at the world economic crisis. The Insider. The New Republic. Robarts Centre for Canadian Studies.