Articlegreen2005

Periodic Stochastic Volatility and Fat Tails

67 citations0/0 files storedJournal of Financial Econometrics

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Financial Risk and Volatility Modeling Financial Markets and Investment Strategies Stochastic processes and financial applications

Abstract

This article provides a comprehensive analysis of the size and statistical significance of the day of the week, month of the year, and holiday effects in daily stock index returns and volatility. We employ data from the Dow Jones Industrial Average (DJIA), the S&P 500, the S&P MidCap 400, and the S&P SmallCap 600 in order to test whether the seasonal patterns of medium and small firms are similar to those of large firms. Using formal hypothesis tests based on bootstrapping, we demonstrate that there are more significant calendar effects in volatility than in expected returns, especially for the two large cap indices. More importantly, we introduce the periodic stochastic volatility (PSV) model for characterizing the observed seasonal patterns of daily financial market volatility. We analyze the interaction between seasonal heteroskedasticity and fat tails by comparing the performance of Gaussian PSV and fat-tailed PSVt specifications to the plain vanilla SV and SVt benchmarks. Consistent with our model-free results, we find strong evidence of seasonal periodicity in volatility, which essentially eliminates the need for a fat-tailed conditional distribution, and is robust to the exclusion of the crash of 1987 outliers.

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References

1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 1987The Pricing of Options on Assets with Stochastic Volatilities 1988A Theory of Intraday Patterns: Volume and Price Variability 1998Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models 1980Stock returns and the weekend effect 1986Stock return variances 1983Size-related anomalies and stock return seasonality 2002Bayesian Analysis of Stochastic Volatility Models

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2006Statistical mechanics of socio-economic systems with heterogeneous agents 2014Long Memory and Periodicity in Intraday Volatility 2009The day-of-the-week effects on the volatility: The role of the asymmetry 2004Properties of realized variance for a pure jump process: calendar time sampling versus business time sampling 2006Pricing multivariate currency options with copulas 2011Financial Economics, Fat-Tailed Distributions

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