Kurtosis

Overview

Kurtosis is a statistical measure from the fourth moment of a distribution that describes the shape of price return distributions, specifically measuring how much of the variance is due to extreme deviations versus moderate fluctuations. In financial markets, kurtosis helps identify periods when prices are more likely to experience extreme movements. A distribution with high kurtosis (leptokurtic) has heavy tails and a sharp peak, indicating higher probability of extreme price movements, while low kurtosis (platykurtic) suggests a flatter distribution with fewer extremes.

Normal distributions have a kurtosis of 3 (or excess kurtosis of 0), providing a baseline for comparison. Values above 3 indicate "fat tails" where extreme events occur more frequently than expected under normal conditions - a critical insight for risk management. Financial markets often exhibit high kurtosis during crisis periods when tail events become more common. Traders use kurtosis to assess market risk, identify regime changes, and adjust position sizing based on the likelihood of tail events. The indicator's ability to quantify the probability of extreme moves makes it particularly valuable for options traders and risk managers who need to account for non-normal distributions in their models.

Interpretation & Trading Signals

Example Usage

Code examples will be available once the Rust implementation is complete.