Stable distributions are suggested as being the underlying distributions for many economic variables. Capital market variables, in particular, are said to follow a member of the symmetric stable class.

This paper examines the implied standard deviation (ISD) estimated from transactons data on options, using the Black-Scholes pricing model. It was found that the distribution of the ISD is symmetric, though not normal. Also, the ISD based on the last daily observation deviates significantly from the daily average ISD. It is suggested that the daily average is a more reliable estimate of the standard deviation.

Edward I. Altman, Menachem Brenner, Information Effects and Stock Market Response to Signs of Firm Deterioration, The Journal of Financial and Quantitative Analysis, Vol. 16, No. 1 (Mar., 1981), pp. 35-51

The objective of this paper is to provide a deeper insight into the links between financial markets and the real economy. To that end, we study the short-term anticipation and response of U.S. stock, Treasury, and corporate bond markets to the first release of surprise U.S. macroeconomic information. Specifically, we focus on the impact of these announcements not only on the level, but also on the volatility and comovement of those assets’ returns. We do so by estimating several extensions of the parsimonious multivariate GARCH-DCC model of Engle (2002) for the excess holding-period returns on seven portfolios of these asset classes. We find that both the process of price formation in each of those financial markets and their interaction appear to be driven by fundamentals. Yet our analysis reveals a statistically and economically significant dichotomy between the reaction of the stock and bond markets to the arrival of unexpected fundamental information. We also show that the conditional mean, volatility, and comovement among stock, Treasury, and corporate bond returns react asymmetrically to the information content of these surprise announcements. Overall, the above results shed new light on the mechanisms by which new information is incorporated into prices within and across U.S. financial markets.