I am looking for ways to estimate volatility. Can anyone please tell me how to estimate the volatility of an instrument at any point of time? Thanks in advance.

I supposed by "estimate" you mean "calculate". I use TR (true range), often referred to as ATR (average true range). It is a key calculation in my trading. On daily bars, I want a stock to have a range from hi-low over a preceeding X number of days. I look for a percentage of this range compared to the stock price. In simple terms, I want a stock to have moved from a 3 day high to a 3 day low at least equivalent to 7% of the stock's price. In my style of trading, I've found it to be an important factor in profitablity.

historical volatility (HV) aka statistical volatility (SV): annualized HV = sqrt[ 252 * variance of natural log differences in daily prices for the calendar month ] source : http://www.cbot.com/cbot/pub/page/0,3181,774,00.html implied volatility (IV): The market's expectation of future price volatility as implied by prevailing option prices ("premiums"). This volatility is measured by entering the premiums into an options pricing model, then solving for volatility. The implied volatility value is based on the mean of the two nearest-the-money calls and the two nearest-the-money puts using the options pricing model. This value is the market's estimate of how volatile the underlying instruments will be from the present until the option's expiration. source : http://www.crbtrader.com/support/options.asp

It's interesting (to me, at least) that there seems to be little agreement concerning the definition of "historical volatility". Many define it as the standard deviation of returns over some time period, but neglect to say if the returns are daily, weekly ... whatever. Further, they neglect to say what time period. Further, even the definition of "standard deviation" varies. Maybe it's or maybe it's Then (again!) there's that volatility definition in terms of the logarithm of prices: annualized historical volatility = square root of ( 250 * variance of log differences in daily prices) ... and since variance = (standard deviation)^2, what standard deviation? Mamma mia!

Daily is the norm. Yeah, this one is all over the place, although the end result usually winds up being annualized. This brings up the key subject of optimal sample size determination for a time series. If you have any ideas, please share. I would choose the sample definition, unless you calculate using the totality of all daily returns since IPO. Not reasonable even for GOOG anymore.

Yeah, that's an interesting one! In my spreadsheets, if the user downloads stock prices over the past N days, I provide the standard deviation of returns for that number of returns. I know of no use for standard deviation (such as Black-Scholes, estimating future prices, buy/sell signals, return distributions, etc.) which require accuracy to, say, 2% ... in which case I can see no good argument for choosing one definition over t'other: 1/n or 1/(n-1) .... for n > 25, the difference in volatility is less than 2% Perhaps the best argument for using the 1/n definition (which is what I use) is all the neat formulas ... especially #6

Does anybody actually use historical volatility in option trading? It seems to me that all the emphasis is on implied volatility, and I've looked but see nowhere anybody is actually using HV, although there is a lot of stuff about how to calculate it.