Dynamic/Adaptive Fee

Volatility-Based Fee Calculation

The dynamic fee system adjusts based on market volatility using the following formula

$fee_{dynamic} = fee_{base} + \alpha \cdot \sigma_{market} + \beta \cdot \Delta P$

Where:

• $fee_{base}$ (minimum fee rate)

• $\alpha$ (volatility sensitivity parameter)

• $\sigma_{market}$ (market volatility measure)

• $\beta$ (price change sensitivity)

• $\Delta P$ (recent price change)

Volatility Estimation

Market volatility is calculated using a rolling window approach:

$\sigma_{market} = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (r_i - \bar{r})^2}$

Where:

• $r_i = \ln\left(\frac{P_i}{P_{i-1}}\right)$ are the logarithmic returns,

• $\bar{r}$ is the mean return over the period,

• $n$ is the window size (number of returns).

Fee Adjustment Formula

The specific fee adjustment can be expressed as:

$fee_{rate} = \min \left( fee_{max}, \; fee_{base} + volatility_{component} \right)$

Where:

$volatility_{component} = \min \left( max_{volatility\_fee}, \; volatility_{factor} \times recent_{price\_volatility} \right)$

And:

$recent_{price\_volatility} = \frac{P_{max} - P_{min}}{P_{avg}}$

Over the last N observations.