Meaning
Statistical process of calculating the shape of the extreme portions of a probability distribution to assess the likelihood of rare events. Accurate tail index estimation is required for any company that wants to survive a black swan event. It provides a numerical value for the risk of a catastrophe.
Lack Evidence
Scarcity of observations in the far reaches of a sample makes the calculation difficult. Tail index estimation must rely on a small number of data points to predict the behavior of events that have not yet happened. This makes the choice of estimator a sensitive part of the process.
Slope Calculation
Gradient of the tail reveals whether the risk is increasing or decreasing as events get larger. Through tail index estimation, a person can see if their business is exposed to the type of volatility that can cause ruin. This shape is a fundamental characteristic of the risk environment.
Risk Projection
Application of the calculated index to set insurance premiums or capital reserves is the final step. Tail index estimation turns a vague fear of the unknown into a specific probability that can be managed. It is the basis for setting the limits on how much risk an organization will take.
