The Basics of Financial Econometrics: Tools, Concepts, and Asset Management Applications

APPENDIX B

Continuous Probability Distributions Commonly Used in Financial Econometrics

In this appendix, we discuss the more commonly used continuous probability distributions are used in financial econometrics. The four distributions discussed are the normal distribution, the chi-square distribution, the Student's t-distribution, the Fisher's F-distribution. It should be emphasized that although many of these distributions enjoy widespread attention in financial econometrics as well as financial theory (e.g., the normal distribution), due to their well-known characteristics or mathematical simplicity, the use of some of them might be ill-suited to replicate the real-world behavior of financial returns. In particular, the four distributions just mentioned are appealing in nature because of their mathematical simplicity, due to the observed behavior of many quantities in finance, there is a need for more flexible distributions compared to keeping models mathematically simple. For example, although the Student's t-distribution that will be discussed in this appendix is able to mimic some behavior inherent in financial data such as so-called fat tails or heavy tails (which means that a lot of the probability mass is attributed to extreme values),¹ it fails to capture other observed behavior such as skewness. For this reason, there has been increased interest in a continuous probability distribution in finance and financial econometrics known as the α-stable distribution. We will ...