Log-Returns

Log-returns are the natural logarithm of the ratio of the price at two different times, commonly used in financial analysis instead of simple percentage returns. They are preferred in quantitative finance because they are time-additive and tend to be more normally distributed than simple returns.

In the context of ARCH and GARCH modeling, log-returns allow for easier mathematical manipulation and more robust statistical analysis. They help normalize the impact of large price swings, making it easier to identify volatility patterns.

For cryptocurrency traders, using log-returns is standard practice for calculating cumulative returns and assessing portfolio performance. They are essential for the accurate application of pricing formulas like Black-Scholes.

By using log-returns, analysts ensure that their models are mathematically consistent and better suited for the complexities of financial derivatives.