Comparing Heavy-Tailed Distributions in Fitting the Canadian Stock Market Returns

Abstract

Much of financial engineering is based on so-called “complete markets” and on the use of the Black-Scholes formula. The formula relies on the assumption that asset prices follow a log-normal distribution, or in other words, the daily fluctuations in prices viewed as percentage changes follow a Gaussian distribution. On the contrary, studies of actual asset prices show that they do not follow a log-normal distribution. In this paper, we investigate several widely-used heavy-tailed distributions. Our results indicate that the Skewed t distribution has the best empirical performance in fitting the Canadian stock market returns. We claim the results are valuable for market participants and the financial industry.