Continuous Probability Distributions with Appealing Statistical Properties

Abstract: To model the behavior of certain financial assets in a stochastic environment, we can usually resort to a variety of theoretical distributions. Most commonly, probability distributions are selected that are analytically well known. For example, the normal distribution is often the distribution of choice when asset returns are modeled, or the exponential distribution is applied to characterize the randomness of the time between two successive defaults of firms in a bond portfolio. Many other distributions are related to them or built on them in a well-known manner. These distributions often display pleasant features such as stability under summation—meaning that the return of a portfolio of assets whose returns follow a certain distribution again follows the same distribution. However, one has to be careful using these distributions since their advantage of mathematical tractability is often outweighed by the fact that the stochastic behavior of the true asset returns is not well captured by these distributions.

In this entry, we discuss the more commonly used distributions ...

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