Publicado
2010-08-28

Una revisión de los modelos de volatilidad estocástica

A revision of stochastic volatility models

DOI: https://doi.org/10.15332/s2027-3355.2010.0001.05
Ronne Tamayo Medina
Heivar Yesid Rodríguez Pinzón

Resumen (es)

En economía, una buena parte de los procesos observados a través del tiempo se plantean como el resultado de efectos de variables latentes, es decir, procesos no observables de forma directa. Este es el caso de la volatilidad de la rentabilidad en el mercado financiero, la cual ha sido modelada desde comienzos de los años 80 empleando modelos de varianza condicional ARCH y GARCH y, más recientemente modelos de volatilidad estocástica SV, los cuales presentan un menor número de parámetros que los modelos GARCH y permiten estudiar la naturaleza no-lineal de la volatilidad.Debido a que en el modelo SV no se conoce de forma exácta la función de verosimilitud, se emplea el método de estimación máximo cuasi-verosímil propuesto por gh94, el cual utiliza la representación en forma de modelo de estados State-Space. La representacion del modelo SV mediante la forma de estados se evalua a traves de filtros adaptativos, como es el caso de los filtros Kalman, lo cual implica un mayor costo computacional. A partir de lo anterior, no necesariamente se llega a la solución óptima del problema.
Palabras clave (es): Filtro Kalman, modelos de estado-espacio, modelos de volatilidad estocástica

Resumen (en)

In economics, a good part of the processes observed over time arise as the result of effects of latent variables, ie processes not directly observable. This is the case of the volatility of financial market returns, which has been shaped since the early 80s using ARCH and GARCH conditional variance models, and more recently stochastic volatility models (SV), which present fewer parameters than GARCH models and allow us to study the non-linear nature of volatility. Because in the SV model is not known accurately the likelihood function, the method of maximum quasi-likelihood is used. This method uses the representation in state-space model form. The SV model representation is evaluated through adaptive filters, such as Kalman, which implies a higher computational cost. 

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Cómo citar

Tamayo Medina, R., & Rodríguez Pinzón, 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