Local Volatility

The traditional calculation of volatility involves computing the standard deviation of returns,
which is based on the mean return. However, when the asset price exhibits a trending behavior,
the mean return could be significantly different from zero, and changing the length of the time
window used for the calculation could result in artificially high volatility values. This is because
more returns would be further away from the mean, leading to a larger sum of squared deviations.
To address this issue, our Local Volatility measure computes the standard deviation of the
differences between consecutive asset prices, rather than their returns. This provides a measure of
how much the price changes from one tick to the next, irrespective of the overall trend.
~ arxiv.org/abs/2308.14235