Log Returns Transformation

Log returns transformation is the process of converting raw price data into logarithmic returns to achieve better statistical properties for analysis. Log returns are defined as the natural logarithm of the ratio of the current price to the previous price.

This transformation is preferred in finance because it is time-additive, meaning the log return over a multi-period horizon is simply the sum of the log returns of the individual periods. Furthermore, log returns are more likely to be normally distributed than raw price changes, which simplifies the application of many statistical models.

In the context of derivatives, log returns are a standard input for Black-Scholes and other pricing models that assume geometric Brownian motion. This transformation helps stabilize the variance of the data, which is crucial for models that assume constant volatility.

By using log returns, traders and researchers can perform more accurate statistical inference and build models that are less affected by the scale of the asset's price. It is a fundamental data preprocessing step that improves the quality and comparability of financial data across different assets and timeframes.