Una revisión de los modelos de volatilidad estocástica.

• Ronne Tamayo Medina ^[1] ; Heivar Yesid Rodriguez Pinzón ^[2]
  1. [1] Universidad Nacional de Colombia

     Universidad Nacional de Colombia

     Colombia

     
  2. [2] Universidad Santo Tomás

     Universidad Santo Tomás

     Santiago, Chile

     
• Localización: Comunicaciones en Estadística, ISSN 2027-3355, ISSN-e 2339-3076, Vol. 3, Nº. 1, 2010, págs. 79-98
• Idioma: español
• DOI: 10.15332/s2027-3355.2010.0001.05
• Títulos paralelos:
  • A revision of stochastic volatility models.
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    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 dela 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 cuasiverosímil propuesto por Geert & Campbell (1994), el cual utiliza la representaci ́on 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.

  • English

    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

• Referencias bibliográficas
  • Aydemir, A. (1998), ‘Forecast performance of threshold autoregressive models a monte carlo study’, UWO. Department of Economics Working Papers.
  • Black, F. & Scholes, M. (1973), ‘The pricing of option and corporate liabilities’, Journal of Political Economy.
  • Bollerslev, T. (1986), ‘Generalized autoregressive conditional heteroscedasticity’, Journal of Econometrics.
  • Breidt, F., Crato, N. & de Lima, P. (1998), ‘The detection and estimation of long memory in stochastic volatility’, Journal of Econometrics.
  • Campbell, J. & Hentschel, L. (1992), ‘An asymmetric model of changing volatility in stocks returns’, Journal of Financial Economics .
  • Davis, M. & Vinter (1985), Stochastic Modelling and Control, Chapman and Hall.
  • Durbin, J. & Harvey, A. (1985), The effects of seat belt legislation on road causalities in great Britain: Report on assessment of the...
  • Engle, R. (1982), ‘Autoregressive conditional heteroskedasticity with estimates of united kingdom inflation’, Econometrica .
  • Fama, E. (1965), ‘The behavior of stocks market prices’, Journal of Business. Figlewski, S. (1997), ‘Forecasting volatility’, Financial Markets,...
  • Garman, M. B. & Klass, M. (1980), ‘On the estimation of security price volatilities from historical data’, Journal of Business.
  • Geert, B. & Campbell, H. (1994), ‘Time-varying world market integration’, NEBER Working Papers (4843).
  • Hannan, E. & Deistler, M. (1988), La Teoría Estadística de Sistemas Lineales, Wiley.
  • Harvey, A. (1994), Forecasting structural time series models and the kalman filter, Cambridge University Press.
  • Hsieh, D. (1995), ‘Nonlinear dynamics in financial markets: Evidence and implica- tions’, Financial Analysts Journal .
  • Li, C. & Li, W. (1996), ‘On a double threshold autoregessive conditional hetero- kedasticity time series model’, Journal Applied Econometrics.
  • Mandelbrot, B. (1963), ‘The variation of certain speculative price’, Journal of Business.
  • Markowitz, H. (1952), ‘Portafolio selection’, The Journal of Finance.
  • Merton, R. (1974), ‘On the pricing of corporate debt: The risk structure of interest rates’, Journal of Finance.
  • Rabemananjara, R. & Zakoian, J. M. (1993), ‘Threshold arch models and asymmetries in volatility’, Journal of Applied Econometrics.
  • Sharpe, W. (1964), ‘Capital asset prices - a theory of market equilibrium under conditions of risk’, Journal Of Finance .
  • Shephard, N. (1986), Time Series Models in Econometrics, Chapman and Hall. Steyn, I. (1996), ‘State space models in econometrics: a field guide’,...
  • Taylor, S. (1986), Modelling Financial time series, John Wiley.
  • Tobin, J. (1958), ‘Liquidity preference as behavior towards risk’, Review of Economic Studies .
  • Tong, H. (1978), On a Threshold Model.