Comfort: A Common Market Factor Non-Gaussian Returns Model

Abstract

A new multivariate time series model with various attractive properties is motivated and studied. By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast EM-algorithm is developed for estimation. Each element of the vector return at time tt is endowed with a common univariate shock, interpretable as a common market factor. This leads to the new model being a hybrid of GARCH and stochastic volatility, but without the estimation problems associated with the latter, and being applicable in the multivariate setting for potentially large numbers of assets. A feasible technique which allows for multivariate option pricing is presented, along with an empirical illustration. AbstractA new multivariate time series model with various attractive properties is motivated and studied.By extending the CCC model in several ways, it allows for all the primary stylized facts of financial asset returns, including volatility clustering, non-normality (excess kurtosis and asymmetry), and also dynamics in the dependency between assets over time. A fast EM-algorithm is developed for estimation. Each element of the vector return at time t is endowed with a common univariate shock, interpretable as a common market factor. This leads to the new model being a hybrid of GARCH and stochastic volatility, but without the estimation problems associated with the latter, and being applicable in the multivariate setting for potentially large numbers of assets. A feasible technique which allows for multivariate option pricing is presented, along with an empirical illustration.

A dominance approach for comparing the performance of VaR forecasting models

“…Among multivariate applications, Hu (2005) develops a method to calibrate a multivariate generalized hyperbolic distribution using the EM algorithm. Paolella and Polak (2015) While the need to consider asymmetric probability distributions for return innovations seems to be well established at this point, the preference for a given volatility specification is less clear. We consider three general volatility models with leverage, GJR-GARCH, APARCH, and FGARCH, with a standard symmetric GARCH model as benchmark.…”

New Graphical Methods and Test Statistics for Testing Composite Normality

“…Q-Q plot for a random N(10, 2) sample of size n = 50 with 10% and 5% pointwise null bands obtained via simulation (top panels), using the estimated parameters (left) and the true parameters (right) of the data. The bottom ones are similar, but based on the asymptotic distribution in (2).…”

Time-Varying Mixture GARCH Models and Asymmetric Volatility

“…For example, a straightforward generalization of MixN-GARCH-LIK is derived, e.g., by using the multivariate mixture GARCH model in Haas et al (2009), given that the process of the mixture weights in (21) is entirely likelihood driven and, hence, generally applicable to univariate as well as multivariate models. Alternatively, it appears possible to augment the EM algorithm approach used for the multivariate mixture-based GARCH model in Paolella and Polak (2013) to the model structure used herein, thus rendering estimation in high dimensions feasible. Another approach which is also feasible in high dimensions is the use of Independent Component Analysis methods.…”