COMFORT: A common market factor non-Gaussian returns model

Abstract

JEL classification: C51 C53 G11 G17 Keywords: CCC Common jumps Density forecasting EM-algorithm Fat tails GARCH Multivariate asymmetric variance gamma distribution Multivariate generalized hyperbolic distribution Multivariate option pricing Stochastic volatility a b s t r a c tA 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.

Forecasting Value-at-Risk under Different Distributional Assumptions

“…The lognormal distribution has also been used to model asset returns, but its skewness is a function of its mean and variance, not a separate parameter. Others, such as the generalized hyperbolic (GH) or mixtures of distributions have also been employed in financial applications, despite being more computationally demanding (see Barndorff-Nielsen [27] for an introduction and Paolella and Polak [28] for a recent application).…”

A GARCH-VaR Investigation on the Brazilian Sectoral Stock Indices

“…Also, the authors perceived that the data sample window plays a crucial role when measuring VaR forecast performance: simple models and low confidence levels benefit from smaller windows (in their experiment, smaller than 2000 observations). In a recent paper, Paolella and Polak (2015) proposed a hybrid GARCH model which allows to deal with volatility clustering, non-normality, and also dynamics in the dependency between assets over time.…”

“…In our study, we decided to model the data by using the usual GARCH modeling because of its computational implementation which seems to be easier than the proposal in Paolella and Polak (2015). It is important to note that, for our proposal, the GARCH-VaR and the proposed coverage tests (Christoffersen, 1998, Candelon et al, 2010 were sufficient to identify the different risk patterns on the Brazilian sectoral stock indices.…”

“…On this way we estimated the VaR 99% (1% VaR) and VaR 1% (99% VaR) by using the most common GARCH specifications, namely, the Normal-GARCH (NGARCH), the tGARCH, and the eGARCH (Nelson, 1991a) approaches. In this sense, although new strategies to estimate VaR have been being proposed (e.g., Chernozhukov (2005), Paolella and Polak (2015)), we understand that the usual GARCH specifications are enough to generate confident estimates focusing on an easy implementation, which does not enforce an exhaustive computational effort. In our study, we highlighted the VaR measure as a risk indicator able to help investors on making a portfolio selection on the Brazilian stock market.…”

Interval Estimation of Value-at-Risk Based on Nonparametric Models

“…EVT (Extreme Value Theory) and the so-called GHYP (Generalized HYPerbolic) distributions are among the most widely used. The main advantage of hypothesizing a GHYP distribution is its ability to account for the statistical properties of financial market data such as volatility clustering, asymmetry and heavy-tail phenomena (see McNeil et al (2005) for an introduction and Paolella and Polak (2015) for a recent application). Kuester et al (2006) use an EVT-based approach and focuses on the long tails of the return distribution.…”