Realized Volatility Calculation

[kinderchocolate]

Hi,

I am confused about the formula for calculating realized or historical volatility over a period of time.

Paul Wilmott claims the formula in his book is:

SQRT(252) * SQRT(AVERAGE_OF_LOG_RETURNS)

But in some other sources, it involves the average variance from the mean, for example

http://www.trade2win.com/boards/attachments/indicators/8907d1090072498-volatility-historical-volatility-calc.doc

Which is right?

Thanks,

 

[PierreXu]

In the case of common stocks, the expectation of daily log return is about zero.

 

[latency]

variance is additive
therefore, number of trading days in a year * square of daily returns =annualized variance., you assume that the mean of these daily returns is zero.
so annualized volatility = average daily return*(252)^.5.

you would change the trading days based on the product you are trading.

 

[iddqd]

The trade 2 win calculation is correct, I am pretty sure that is what Wilmott must have meant also.

 

[kinderchocolate]

Thanks, I wasn't expecting that the mean was assumed to be zero.

 

[quotes]

In finance, we don't care about how the drift udt might vary over time, so it is good to have a volatility estimate independent of time drift estimate. True, you can use a R=udt+sdW to estimate s, but at the same time you assume u holds constant among your sample and estimate of s is based on that. Thus Wilmott's or Shreve's method derived from Ito's Calculus is preferable.

 

[DVV]

Hi,

I am confused about the formula for calculating realized or historical volatility over a period of time.

Paul Wilmott claims the formula in his book is:

SQRT(252) * SQRT(AVERAGE_OF_LOG_RETURNS)

But in some other sources, it involves the average variance from the mean, for example

http://www.trade2win.com/boards/att...498-volatility-historical-volatility-calc.doc

Which is right?

Thanks,

well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob.

 

[amir]

Hi,

I am confused about the formula for calculating realized or historical volatility over a period of time.

Paul Wilmott claims the formula in his book is:

SQRT(252) * SQRT(AVERAGE_OF_LOG_RETURNS)

it must be SQRT(252) * SQRT(AVERAGE_OF_SQUARED_LOG_RETURNS)

because AVERAGE_OF_LOG_RETURNS is about zero
now this and the one in trade2win are the same

 

[amir]

well, i see no contradiction. You have formula from Wilmott, it involves Std Dev. Std Dev is calculated from sample Var. Sample VAr is calculated as sum of squared deviations from mean. What the problem? It is basic stat/prob.

Sample var is calculated as average of squared deviations from mean, not sum.

 

[financeguy]

so i think the question is coming down to the subtraction of mean returns.. technically when calculating this historical volatility, or standard deviation, you should subtract the mean return in the formula.. HOWEVER, it is market convention for the payout of volswaps and varswaps to NOT use this mean subtraction term, i.e. the payout is just calculated as the annualized average sum of squared log returns, which is not actually a proper standard deviation calculation, and so this is also of course what the pricing and risk management is based on .. maybe this is what's causing confusion? i'm not sure what context you pulled this reference out of

 

[DVV]

Sample var is calculated as average of squared deviations from mean, not sum.

i see, thanks. well average of returns is often missed just because of convenience. average is pretty small and it is assumed to be zero. when you calculate sample var you should divide by n-1, but again for convenience you divide just by N. After that you get average of squared returns. when you change N-1 to N you get some bias (as i remember), but any case difference is insignificantly small.