Serving the Quantitative Finance Community

User avatar
Topic Author
Posts: 5
Joined: August 31st, 2006, 4:18 am

the volatility of return

September 19th, 2006, 2:34 pm

If the dataset of return is not evenly, for example, is not daily, or monthly data, how we could calculate the volatility?
User avatar
Posts: 134
Joined: July 13th, 2006, 1:05 pm

the volatility of return

October 2nd, 2006, 5:36 pm

You could either throw away some datapoints to make it evenly distributed, or you could extrapolate information by rescaling your dataset to a nearby dataset that is evenly distributed. I am sure there are other ways to work around it, depending on how accurate your result has to be
User avatar
Posts: 37
Joined: January 30th, 2006, 4:01 pm

the volatility of return

October 4th, 2006, 2:16 am

There is something called move based volatility estimation, you can find more information on the web. I think the main result is vol=alpha*sqrt[V(alpha,T)/T] where V(alpha,T) is the number of times that ln(S) moves by alpha.
User avatar
Posts: 23951
Joined: September 20th, 2002, 8:30 pm

the volatility of return

October 4th, 2006, 9:34 pm

You would expect the wider-spaced data points to show greater movement. If you assume IID movements and defined variance, then you would expect the volatility-induced movement during an N-period interval to be SQRT[N] times greater. Thus, you could divide the more widely spaced data points by 1/SQRT(N) to normalize them for unequal spacing. This is a crude approximation as it also divides the drift or average daily gain by that factor. If you want avoid this, then subtract the estimated drift from the data and then normalize by 1/SQRT(N)If you really get into this concept you must start asking if the gap between data points over the week-end or holiday is the same as the gap between successive days (its not). This can lead to interesting ideas about market speed in which changes in volatility can be thought of as changes in a relative timebase. With that interpretation, high volume periods are often "faster" than low volume periods. That is, more market time passes per calendar time on intense days.