Log Returns

Log returns represent the natural logarithm of the ratio of an asset's price at two different points in time. In quantitative finance, log returns are preferred over simple percentage returns because they are time-additive and often exhibit properties closer to a normal distribution.

This mathematical transformation is crucial for volatility modeling, as it allows for the compounding of returns over multiple periods. When analyzing cryptocurrency price series, log returns help normalize the data, making it easier to perform statistical analysis.

By using log returns, researchers can aggregate volatility across different time horizons without introducing bias. This approach is standard in derivative pricing models, such as Black-Scholes, which assume returns are log-normally distributed.

It simplifies the calculation of realized volatility by allowing the summation of squared returns. Consequently, log returns are the building block for most volatility estimators.

They provide a robust framework for comparing the performance of different assets. Using them ensures that statistical models remain consistent and theoretically sound.