how do you do an exponential moving average vol calculation?

[mizhael]

Hi all,

I know how to calculate the EMA:

EMA_t = a*EMA_{t-1} + (1-a)*P_t

but how to calculate the EMVol (exponential moving volatility or standard deviation)?

It cannot be:

EMVol_t^2 = a*EMVol_{t-1}^2 + (1-a)*P_t^2,

because this is assuming the mean is zero.

I was thinking about the following:

EMVariance_t^2 = a*EMVariance_{t-1}^2 + (1-a)*P_t^2,
EMA_t = a*EMA_{t-1} + (1-a)*P_t,

then

EMVol_t^2 = EMVariance_t^2 - EMA_t^2

then we obtain EMVol_t.

Any comments?

 

[Stoxtrader]

Dude. Stdev is just the mean divided by the number of items. Or divided by (number of items minus one) when the number is less than twenty.

...

your list of numbers: 1, 3, 4, 6, 9, 19

mean: (1+3+4+6+9+19) / 6 = 42 / 6 = 7

list of deviations: -6, -4, -3, -1, 2, 12

squares of deviations: 36, 16, 9, 1, 4, 144

sum of deviations: 36+16+9+1+4+144 = 210

divided by one less than the number of items in the list: 210 / 5 = 42

square root of this number: square root (42) = about 6.48

 

[Stoxtrader]

Quote from Stoxtrader:

Dude. Stdev is just the mean divided by the number of items. Or divided by (number of items minus one) when the number is less than twenty.

Gah. Of course I meant to say the sum of the squared deviations divided by the number of items.