Estimación de modelos de volatilidad estocástica vía filtro auxiliar de partículas

• TROSEL, YENIREE ^[1] ; HERNÁNDEZ, ARACELIS ^[2] ; INFANTE, SABA ^[2]
  1. [1] Universidad de Carabobo

     Universidad de Carabobo

     Venezuela

     
  2. [2] Universidad Yachay Tech

     Universidad Yachay Tech

     Urcuqui, Ecuador

     
• Localización: Revista de Matemática: Teoría y Aplicaciones, ISSN 2215-3373, ISSN-e 2215-3373, Vol. 26, Nº. 1, 2019, págs. 45-81
• Idioma: español
• DOI: 10.15517/rmta.v26i1.36221
• Títulos paralelos:
  • Estimation of stochastic volatility models via auxiliary particles filter
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    El creciente interés en el estudio de la volatilidad para series de instrumentos financieros nos lleva a plantear una metodología basada en la versatilidad de los métodos Monte Carlo Secuencial (MCS) para la estimación de los estados del modelo de volatilidad estocástica general (MVEG). En este trabajo se propone una metodología basada en la estructura espacio estado aplicando técnicas de filtrado como es el caso del filtro auxiliar de partículas para la estimación de la volatilidad subyacente del sistema. Adicionalmente, se propone utilizar un algoritmo Monte Carlo por cadenas de Markov (MCMC), como es el muestreador de Gibbs para la estimación de los parámetros. La metodología es ilustrada usando una serie de retornos de datos simulados, y la serie de retornos correspondiente al índice de precio Standard and Poor’s 500 (S&P 500) para el periodo 1995−2003. Los resultados evidencian que la metodología propuesta permite explicar adecuadamente la dinámica de la volatilidad cuando existe una respuesta asimétrica de esta ante un shock de diferente signo, concluyendo que los cambios bruscos en los retornos corresponden a valores altos en la volatilidad.

  • English

    The growing interest in the study of volatility for series of financial instruments leads us to propose a methodology based on the versatility of the Sequential Monte Carlo (SMC) methods for the estimation of the states of the general stochastic volatility model (GSVM). In this paper, we proposed a methodology based on the state space structure applying filtering techniques such as the auxiliary particles filter for estimating the underlying volatility of the system. Additionally, we proposed to use a Markovchain Monte Carlo (MCMC ) algorithm, such as is the Gibbs sampler for the estimation of the parameters. The methodology is illustrated through a series of returns of simulated data, and the series of returns corresponding to the Standard and Poor’s 500 price index (S&P 500) for the period 1995 − 2003. The results show that the proposed methodology allows to adequately explain the dynamics of volatility when there is an asymmetric response of this to a shock of a different sign, concluding that abruptchanges in returns correspond to high values in volatility.

• Referencias bibliográficas
  • Black, F.; Scholes, M. (1973) “The pricing of options and corporate liabilities”, The Journal of Political Economy 81(3): 637–654.
  • Carneiro, P.; Hansen, K.; Heckman, J. (2003) “Estimating distributions of treatment effects with an application to the returns to schooling...
  • Chib, S.; Nardari, F.; Shephard, N. (2002) “Markov chain Monte Carlo methods for stochastic volatility models”,Journal of Econometrics 108(2):...
  • Clark, P. (1973) “A subordinated stochastic process model with finite variance for speculative prices”, Econometrica 41(1): 135–155.
  • Danielsson, J. (1994) “Stochastic volatility in asset prices: estimation with simulated maximum likelihood”, Journal of Econometrics 64: 375–400.
  • Danielsson, J.; Richard, J. F. (1993) “Accelerated gaussian importance sampler with application to dynamic latent variable models”, Journal...
  • Del Moral, P.; Doucet, A. (2003) “On a class of genealogical and interacting metropolis models”, in: J. Azéma, M. Emery, M. Ledoux & M....
  • Doucet, A.; De Freitas, N.; Gordon, N. (2001) “An introduction to sequential Monte Carlo methods”, in: A. Doucet, N. De Freitas & N. Gordon...
  • Doucet, A.; Johansen, A. (2011) “A tutorial on particle filtering and smoothing: fifteen years later”, in: D. Crisan & B. Rozovskii (Eds.)...
  • Gallant, A.; Hsieh, D.; Tauchen, G. (1991) “On fitting a recalcitrant series: the pound/dollar exchange rate, 1974–1983”, in: W. Bartnett,...
  • Ghysels,E.;Harvey,A.C.;Renault,E.(1996)“Stochastic volatility”,in: C. R.Rao & G.Maddala(Eds.) Statistical Models in Finance,North-Holland,...
  • Gordon, N. J.; Salmond, D. J.; Smith, A. F. M. (1993) “Novel approach to nonlinear/non-Gaussian Bayesian state estimation”, IEE Proceedings-F...
  • Harvey,A.;Ruiz,E.;Shephard,N.(1994)“Multivariate stochastic variance models”, The Review of Economic Studies 61(2): 247–264.
  • Heidelberger, P.; Welch, P. (1983) “Simulation run length control in the presence of an initial transient”, Operations Research 31 (6):1109–1144.
  • Hull,J.;White,A.(1987)“The pricing of options on assets with stochastic volatilities”, The Journal of Finance 42(2): 281–300.
  • Isard,M.;Blake,A.(1998)“Condensation-conditional density propagation for visual tracking”, International Journal of Computer Vision 29 (1):...
  • Jacquier, E.; Polson, N.; Rossi, P. (1994) “Bayesian analysis of stochastic volatility models”, Journal of Business and Economic Statistics...
  • Kim, S.; Shephard, N.; Chib, S. (1998) “Stochastic volatility: likelihood inference and comparison with ARCH models”, The Review of Economic...
  • Latané, H.; Rendleman, R. (1976) “Standard deviations of stock price ratios implied in option prices”, The Journal of Finance 31(2): 369–381.
  • Liu, J. S. (2001) Monte Carlo Strategies in Scientific Computing.Springer, New York.
  • Liu, J. S.; Chen, R. (1998) “Sequential Monte Carlo methods for dynamic systems”, Journal of the American Statistical Association 93 (443):...
  • Omori,Y.;Chib,S.; Shephard,N.; Nakajima,J. (2007) “Stochastic volatility with leverage: fast and efficient likelihood inference”, Journal of...
  • Pitt, M.; Shephard, N. (1999) “Filtering via simulation: auxiliary particle filters”, Journal of the American Statistical Association 94 (446):...
  • Shephard, N.; Pitt, M.K. (1997) “Likelihood analysis of non-Gaussian measurement time series”, Biometrika 84(3): 653–667.
  • Shephard, N. (2005) Stochastic Volatility: Selected Readings. Oxford University Press, United States
  • Tauchen, G.; Pitt, M. (1983) “The price variability-volume relationship on speculative markets”, Econometrica 51(2): 485–505.
  • Taylor, S. (1986) Modelling Financial Time Series. John Wiley & Sons, New York.
  • Watanabe, T. (1999) “A non-linear filtering approach to stochastic volatility models with an application to daily stock returns”, Journal of...
  • Yu, J. (2005) “On leverage in a stochastic volatility model”, Journal of Econometrics 127(2): 165–178.