Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness

Mukhoti, Sujay (2014): Non-Stationary Stochastic Volatility Model for Dynamic Feedback and Skewness.

Abstract

In this paper I present a new single factor stochastic volatility model for asset return observed in discrete time and its latent volatility. This model unites the feedback effect and return skewness using a common factor for return and its volatility. Further, it generalizes the existing stochastic volatility framework with constant feedback to one with time varying feedback and as a consequence time varying skewness. However, presence of dynamic feedback effect violates the weak-stationarity assumption usually considered for the latent volatility process. The concept of bounded stationarity has been proposed in this paper to address the issue of non-stationarity. A characterization of the error distributions for returns and volatility is provided on the basis of existence of conditional moments. Finally, an application of the model has been explained using S&P100 daily returns under the assumption of Normal error and half Normal common factor distribution.

• Item Type: MPRA Paper
• Language: English
• Keywords: Stochastic volatility, Bounded stationarity, Leverage, Feedback, Skewness, Single factor model
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C11 - Bayesian Analysis: General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics

References

Aas, K., & Haff, I. H. (2006), “The generalized hyperbolic skew Student’s t-distribution,” Journal of Financial Econometrics, 4(2), 275–309.

Abanto-Valle, C. A., Bandyopadhyay, D., Lachos, V. H., & Enriquez, I. (2010), “Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions,” Computational Statistics and Data Analysis, 54(12), 2883–2898.

Azzalini, A., & Dalla Valle, A. (1996), “The multivariate skew-normal distribution,” Biometrika, 83(4), 715–726.

Berg, A., Meyer, R., & Yu, J. (2004), “Deviance Information Criterion for Comparing Stochastic Volatility Models,” Journal of Business and Economic Statistics, 22(1), 107– 120.

Blair, B., Poon, S., & Taylor, S. (2001), “Modelling S&P100 Volatility: The Information Content of Stock Returns,” Journal of Banking and Finance, 25, 1665 1679.

Bollerslev, T., Litvinova, J., & Tauchen, G. (2006), “Leverage and feedback effects in high frequency data,” Journal of Financial Econometrics, 4, 353–384.

Bollerslev, T., Sizova, N., & Tauchen, G. (2012), “Volatility in Equilibrium: Asymmetries and Dynamic Dependencies,” Review of Finance, 16, 31–80.

Boyer, B., Mitton, T., & Vorkink, K. (2010), “Expected Idiosyncratic skewness,” The Review of Financial Studies, 23(1), 169–202.

CBOE (2009), “The CBOE Volatility Index- VIX,” http://www.cboe.com/micro/vix/vixwhite.pdf, .

Chib, S., Nardari, F., & Shephard, N. (2002), “Markov chain Monte Carlo methods for stochastic volatility models,” Journal of Econometrics, 108(2), 281–316.

Chib, S., Omori, Y., & Asai, M. (2009), “Multivariate Stochastic Volatility,” in Handbook of Financial Time Series, eds. T. Mikosch, J.-P. Krei, R. A. Davis, & T. G. Andersen, Berlin Heidelberg: Springer, pp. 365–400.

Christoffersen, P., Heston, S., & Jacobs, K. (2006), . Eraker, B., Johanners, M., & Polson, N. G. (2003), “The impact of jumps in volatility and returns,” Journal of Finance, 53(3), 1269–1300.

Feunou, B., & T´edongap, R. (2012), “A stochastic volatility model with conditional skewness,” Journal of Business & economic statistics, 30(4), 576–591.

French, R. K., Schwert, G. W., & Stambaugh, F. R. (1987), “Expected Stock Returns and Volatility,” Journal of Financial Economics, 19, 3–29.

Gelman, A., & Rubin, D. (1992), “Inference from Alternative Simulation Using Multiple Sequences,” Statistical Science, 7, 457–472.

Harvey, A. C., Ruiz, E., & Shephard, N. (1994), “Multivariate stochastic variance models,” Review of Economic Studies, 61, 247–264.

Harvey, C., & Siddique, A. (1999), “Autoregressive conditional skewness,” Journal of Finance and Quantitative Analysis, 34, 465–487.

Jacquier, E., Polson, N. G., & Rossi, P. E. (1994), “Bayesian analysis of stochastic volatility models,” Journal of Business and Economic Statistics, 12, 371–389.

Jacquier, E., Polson, N. G., & Rossi, P. E. (2004), “Bayesian analysis of stochastic volatility models with fat-tails and correlated errors,” Journal of Econometrics, 122(1), 185–212.

Kim, S., Shephard, N., & Chib, S. (1998), “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,” Review of Economic Studies, 65(3), 361–393.

Meyer, R., & Yu, J. (2000), “BUGS for a Bayesian analysis of stochastic volatility models,” Econometrics Journal, 3(2), 198–215.

Nelson, B. D. (1991), “Conditional heteroskedasticity in asset pricing: a new approach,” Econometrica, 59, 347–370.

Renault, E. (2009), “Moment Based Estimation of Stochastic Volatility Models,” in Handbook of Financial Time Series, eds. T. Mikosch, J.-P. Krei, R. A. Davis, & T. G. Andersen, Berlin Heidelberg: Springer, pp. 269–311.

Shephard, N., & Andersen, G. (2009), “Stochastic Volatility: Origins and Overview,” in Handbook of Financial Time Series, eds. T. Mikosch, J.-P. Krei, R. A. Davis, & T. G. Andersen, Berlin Heidelberg: Springer, pp. 237–254.

Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002), “Bayesian measures of model complexity and fit,” Journal of the Royal Statistical Society. Series B: Statistical Methodology, 64(4), 583–616.

Taylor, S. J. (1982), “Financial returns modelled by the product of two stochastic processes a study of daily sugar prices 1961-79,” in Time Series Analysis: Theory and Practice 1, ed. O. D. Anderson, Amsterdam: North-Holland, pp. 203–226.

Tsiotas, G. (2012), “On generalised asymmetric stochastic volatility models,” Computational Statistics and Data Analysis, 56(1),