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The problem with what I do above is that I change the unit of time, as opposed to keeping the same unit of time and comparing the different frequencies.

We want to compare the returns over different hedging frequencies, the easy way is to use log return over different frequencies:

$dr_{t}=-\frac{s^2*t}{2} + s*\sqrt{t}*\epsilon∼N(-\frac{s^2∗t}{2},s^2∗t)$

If you do the rest of the math you will get the effect of the expected Gamma PnL and its variance.

The problem with what I do above is that I change the unit of time, as opposed to keeping the same unit of time and comparing the different frequencies.

We want to compare the returns over different hedging frequencies, the easy way is to use log return over different frequencies:

$dr_{t}=-\frac{s^2*t}{2} + s*\sqrt{t}*\epsilon∼N(-\frac{s^2∗t}{2},s^2∗t)$

If do the rest of the math you will the effect of the expected Gamma PnL and its variance.

The problem with what I do above is that I change the unit of time, as opposed to keeping the same unit of time and comparing the different frequencies.

We want to compare the returns over different hedging frequencies, the easy way is to use log return over different frequencies:

$dr_{t}=-\frac{s^2*t}{2} + s*\sqrt{t}*\epsilon∼N(-\frac{s^2∗t}{2},s^2∗t)$

If you do the rest of the math you will get the effect of the expected Gamma PnL and its variance.

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source | link

The problem with what I do above is that I change the unit of time, as opposed to keeping the same unit of time and comparing the different frequencies.

We want to compare the returns over different hedging frequencies, the easy way is to use log return over different frequencies:

$dr_{t}=-\frac{s^2*t}{2} + s*\sqrt{t}*\epsilon∼N(-\frac{s^2∗t}{2},s^2∗t)$

If do the rest of the math you will the effect of the expected Gamma PnL and its variance.