Hi,I created a time series by modelling the returns (1+DRIFT*TIMESTEP+VOL*SQRT(TIMESTEP)*RANDOM) of a stock.Then I tried to see whether the actual volatility of the time series would equal to the volatility I used to model the time series.However they are not equal, does anyone know why this is the case?Regards,

QuoteOriginally posted by: brianhcloHi,I created a time series by modelling the returns (1+DRIFT*TIMESTEP+VOL*SQRT(TIMESTEP)*RANDOM) of a stock.Then I tried to see whether the actual volatility of the time series would equal to the volatility I used to model the time series.However they are not equal, does anyone know why this is the case?Regards,They should be equal. How did you generate the time series and how did u then estimate the volatility ?

QuoteOriginally posted by: brianhcloHi,I created a time series by modelling the returns (1+DRIFT*TIMESTEP+VOL*SQRT(TIMESTEP)*RANDOM) of a stock.Then I tried to see whether the actual volatility of the time series would equal to the volatility I used to model the time series.However they are not equal, does anyone know why this is the case?Regards,I suspect that you measured volatility by the standard deviation. This is not compatible with the forumla you use. To measure the volatility oif the time series in a way that corresponds to the volatility in your forumula, you need to subtract out the drift first.

Subtract the drift? Huh?The vol of any one realization will never be equal to the vol used to generate the series - it's a random process!If you generate many such series, and then take the average, it will come close to the sigma.Drift has nothing to do with it, since:SD(X) = SD(X + C)where X is a random variable, and C is not.

Thanks alot for your info.It makes alot of sense.Brian

Something is not clear in what you say on computing the volatility of the series. You should do this by calculating the st dev of log returns and not of prices.Then you should generate enough prices to have it converge. The convergence speed should be in sqrt (1/N) where N is the number of simulated prices, so with 100,000 prices you should have a very good approximation !!

QuoteOriginally posted by: slegerSomething is not clear in what you say on computing the volatility of the series. You should do this by calculating the st dev of log returns and not of prices.Then you should generate enough prices to have it converge. The convergence speed should be in sqrt (1/N) where N is the number of simulated prices, so with 100,000 prices you should have a very good approximation !!Off course I am calculating the sd of log returns. I was trying to look at the rolling volatility of the time series to see if its a constant (the same as the one I used to generate). But I forgot the fact that the Random term will make the volatility non constant over a short period of time.