Conditionally heteroskedastic factor models with skewness and leverage effects

Dovonon, Prosper (2008): Conditionally heteroskedastic factor models with skewness and leverage effects.

Abstract

Conditional heteroskedasticity, skewness and leverage effects are well known features of financial returns. The literature on factor models has often made assumptions that preclude the three effects to occur simultaneously. In this paper I propose a conditionally heteroskedastic factor model that takes into account the presence of both the conditional skewness and leverage effects. This model is specified in terms of conditional moment restrictions and unconditional moment conditions are proposed allowing inference by the generalized method of moments (GMM). The model is also shown to be closed under temporal aggregation. An application to daily excess returns on sectorial indices from the U.K. stock market provides a strong evidence for dynamic conditional skewness and leverage with a sharp efficiency gain resulting from accounting for both effects. The estimated volatility persistence from the proposed model is lower than that estimated from models that rule out such effects. I also find that the longer the returns’ horizon, the fewer conditionally heteroskedastic factors may be required for suitable modeling and the less strong is the evidence for dynamic leverage. Some of these results are in line with the main findings of Harvey and Siddique (1999) and Jondeau and Rockinger (2003), namely that accounting for conditional skewness impacts the persistence in the conditional variance of the return process.

• Item Type: MPRA Paper
• Language: English
• Keywords: Factor models; conditional heteroskedasticity; conditional leverage; conditional skewness; temporal aggregation; generalized method of moments
• Subjects: C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Alami, A. and Renault, E. (2001). Risque de modele de volatilite. Working Paper. CIRANO. Ref. 2001s-06.

Andersen, T. G. (1994). Stochastic autoregressive volatility: A framework for volatility modeling. Mathematical Finance, 4:75–102.

Black, F. (1976). Studies of stock market volatility changes. 1976 Proceedings of the American Statistical Association, Business and Economic Statistics Section, pages 177–181.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31:307–327.

Brandt, M. W. and Diebold, F. X. (2006). A no-arbitrage approach to range-based estimation of return covariances and correlations. Journal of Business, 79:61–73.

Broto, C. and Ruiz, E. (2004). Estimation methods for stochastic volatility models: A survey. Journal of Economic Surveys, 18:613–649.

Christoffersen, P., Heston, S., and Jacobs, K. (2006). Option valuation with conditional skewness. Journal of Econometrics, 131:253–284.

Cox, J. C., J. E. Ingersoll, J., and Ross, S. A. (1985). A theory of term structure of interest rates. Econometrica, 53-2:385–408.

Dai, Q. and Singleton, K. (2000). Specification analysis of affine term structure models. Journal of Finance, 55:1943–1978.

Diebold, F. and Nerlove, M. (1989). The dynamics of exchange rate volatility: A multivariate latent factor arch model. Journal of Applied Econometrics, 4:1–21.

Dovonon, P. (2012). Supplement to “conditionally heteroskedastic factor models with skewness and leverage effects”. Concordia University.

Doz, C. and Renault, E. (2006). Factor volatility in mean models: a gmm approach. Econometric Reviews, 25:275–309.

Drost, F. C. and Nijman, T. E. (1993). Temporal aggregation of garch processes. Econometrica, 61:909–927.

Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of variance of United Kingdom inflation. Econometrica, 50:987–1007.

Engle, R. F. (2002). Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroscedasticity models. Journal of Business and Economic Statistics, 20:339–350.

Engle, R. F. and Ng, V. K. (1993). Measuring and testing the impact of news on volatility. Journal of Finance, 48:1749–1778.

Engle, R. F. and Patton, A. J. (2001). What good is a volatility model? Quantitative Finance, 1:237–245.

Fiorentini, G., Sentana, E., and Shephard, N. (2004). Likelihood-based estimation of generalised arch structures. Econometrica, 72:1481–1517.

Glosten, L. R., Jaganathan, R., and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on shocks. Journal of Finance, 48:1779–1801.

Hansen, L. P. (1982). Large properties of generalized method of moments estimators. Econometrica, 50:1029–1054.

Harvey, A., Ruiz, E., and Sentana, E. (1992). Unobserved component time series models with arch disturbances. Journal of Econometrics, 52:129–157.

Harvey, C. R. and Siddique, A. (1999). Autoregressive conditional skewness. Journal of Financial and Quantitative Analysis, 34:465–487.

Harvey, C. R. and Siddique, A. (2000). Conditional skewness in asset pricing tests. Journal of Finance, 55:1263–1295.

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.

Heston, S. L. and Nandi, S. (2000). A closed-form garch option pricing model. Review of Financial Studies, 13-3:585–625.

Jondeau, E. and Rockinger, M. (2003). Conditional volatility, skewness, and kurtosis: Existence, persistence, and comovements. Journal of Economic Dynamics and Control, 27:1699–1737.

King, M. A., Sentana, E., and Wadhwani, S. B. (1994). Volatility and links between national stock markets. Econometrica, 62:901–933.

Kraus, A. and Litzenberger, R. (1976). Skewness preference and valuation of risk assets. Journal of Finance, 31:1085–1100.

Manski, C. F. and Tamer, E. (2002). Inference on regressions with interval data on a regressor or outcome. Econometrica, 70:519–546.

Meddahi, N. and Renault, E. (1997). Aggregations and marginalization of garch and stochastic volatility models. Working Paper. Universite de Montreal.

Meddahi, N. and Renault, E. (2004). Temporal aggregation of volatility models. Journal of Econometrics, 119:355–379.

Melino, A. and Turnbull, S. (1990). Pricing foreign currency options with stochastic volatility. Journal of Econometrics, 45:239–265.

Mencia, J. and Sentana, E. (2012). Distributional tests in multivariate dynamic models with normal and student t innovations. Review of Economics and Statistics, 94:133–152.

Nelson, D. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica, 59:347–370.

Rubinstein, M. E. (1973). The fundamental theorem of parameter-preference security valuation. Journal of Financial and Quantitative Analysis, 8:61–69.

Sentana, E. (1995). Quadratic garch models. Review of Economic Studies, 62:639–661.

Sentana, E., Calzolari, G., and Fiorentini, G. (2008). Indirect estimation of conditionally heteroscedastic factor models. Journal of Econometrics, 146:10–25.

Sentana, E. and Fiorentini, G. (2001). Identification, estimation and testing of conditionally heteroscedastic factor models. Journal of Econometrics, 102:143–164.

Singleton, K. (2001). Estimation of affine asset pricing models using the empirical characteristic function. Journal of Econometrics, 102:111–141.

Sorenson, H. W. (1985). Kalman Filtering: Theory and Application. IEEE Press.

Taylor, S. J. (1986). Modeling Financial Time Series. John Wiley.