What happens when the stock markets are closed

Abstract

The normality of the log-return of stock prices is often assumed by the market players in order to use some useful results, as for instance, the Black-Scholes formula for pricing European options. However, several studies regarding different indexes have shown that the normality assumption of the returns usually fails. In this paper we analyse the normality assumption for intra-day and inter-day log-returns, comparing opening prices and/or closing prices for a large number of companies quoted in the Nasdaq Composite index. We use the Pearson's Chi-Square, Kolmogorov-Smirnov, Anderson-Darling, Shapiro-Wilks and Jarque-Bera goodness-of-fit tests to study the normality assumption.We find that the failure rate in the normality assumption for the log-return of stock prices is not the same for intra-day and inter-day prices, is somewhat test dependent and strongly dependent on some extreme price observations. To the best of our knowledge, this is the first study on the normality assumption for the log-return of stock prices dealing simultaneously with a large number of companies and normality tests, and at the same time considering various scenarios of intra-day, inter-day prices and data trimming.