U.S. Stock Market Crash Risk, 1926-2006
This paper applies the Bates (RFS, 2006) methodology to the problem of estimating and filtering time- changed Lévy processes, using daily data on U.S. stock market excess returns over 1926-2006. In contrast to density-based filtration approaches, the methodology recursively updates the associated conditional characteristic functions of the latent variables. The paper examines how well time-changed Lévy specifications capture stochastic volatility, the "leverage" effect, and the substantial outliers occasionally observed in stock market returns. The paper also finds that the autocorrelation of stock market excess returns varies substantially over time, necessitating an additional latent variable when analyzing historical data on stock market returns. The paper explores option pricing implications, and compares the results with observed prices of options on S&P 500 futures.
I am grateful for comments on earlier versions of the paper from seminar participants at Iowa, Turin, Birkbeck, McGill's 2008 Risk Management Conference, the 18th Annual Derivatives Securities and Risk Management Conference in Arlington, VA, and Princeton's 2008 Conference on Implied Volatility Models. I also thank Ken French for providing the stock turnover data from French (2008). The views expressed herein are those of the author(s) and do not necessarily reflect the views of the National Bureau of Economic Research.