Hi there...A few nebie questions regarding volatility modelling... 1) Let's say I'm building a model for forecasting volatility to be used in option pricing. Which measure of volatility should I use as a reference for assesing the "quality" of a model, i.e. precision of forecasts? 2) Is there a consensus on the distinction between historical and realised volatility? Reading this forum I noticed some people seem to consider the two are the same, others don't. Can somebody explain this?3) Let's say I'm interested in FX volatility. How reasonable it is to calculate 5-day volatility with close-to-close exchange rate values? How reasonable is it to use intraday volatilities for this period? And how about 20+ days volatility: close-to-close exchange rate vs. intraday volatility? 4) Are there methods to calculate volatility of an asset considering the values of its high/low daily bids?5) Let's say I want to model a volatility of an FX rate using GARCH. I have a historic series of daily rates, let's say I want to model 20 day volatility of an exchange rate. Am I right to assume I would first need to convert the series into a rolling 20-day historical volatility series, and then feed that to GARCH? If not, what do I do?Thanks a lot,srdjan

(0) These questions are in the wrong place. They belong in the General or Technical forum, not Numerical Methods. (1) See the literature. Start with Christie (1982), Canina and Figlewski (1993), etc.(2) To many people historical and realized volatility are the same. In the F. X. Diebold and T. Andersen paper(s) such as "the distribution of realized stock volatility" (2001) "modeling and forecasting realized volatility" (2002), etc. the term "realized volatility" is used for a volatility based on very short term (e.g. intraday, say half hour interval) observations. However, as you point out, some people do not make this distinction. We will see if it catches on or not.(3) A historical volatility based on 5 closing prices would seem to be an extremely noisy estimator. Even a 21 day closing price vol has, if I recall correctly a 50% sampling error! (based on the Chi Square distribution). I consider a 21 day historical vol to be near the lower limit of usefulness. I suggest you use use more than 5 obs, either closing price or intraday. The secret of historical vol estimation is "the more observations the better".(4) This is called the Parkinson Estimator of vol, based on highs and lows. Please Google.(5) These models are usually estimated using maximum likelihood. Based on the data (daily returns) and assumed values of the parameters, the value of the Likelihood Function is computed. Then the parameter values are changed to see if the LF can be improved. When the LF seems to have reached a maximum you stop and take these parameter values to be your estimated GARCH parameters. Once these parameters are estimated a 20 day (or whatever) forecast can be made. See the GARCH appendix in F.X. Diebold's book "Elements of forecasting" for details and an example.

QuoteOriginally posted by: SrlleHi there...A few nebie questions regarding volatility modelling... 1) Let's say I'm building a model for forecasting volatility to be used in option pricing. Which measure of volatility should I use as a reference for assesing the "quality" of a model, i.e. precision of forecasts? 2) Is there a consensus on the distinction between historical and realised volatility? Reading this forum I noticed some people seem to consider the two are the same, others don't. Can somebody explain this?3) Let's say I'm interested in FX volatility. How reasonable it is to calculate 5-day volatility with close-to-close exchange rate values? How reasonable is it to use intraday volatilities for this period? And how about 20+ days volatility: close-to-close exchange rate vs. intraday volatility? 4) Are there methods to calculate volatility of an asset considering the values of its high/low daily bids?5) Let's say I want to model a volatility of an FX rate using GARCH. I have a historic series of daily rates, let's say I want to model 20 day volatility of an exchange rate. Am I right to assume I would first need to convert the series into a rolling 20-day historical volatility series, and then feed that to GARCH? If not, what do I do?Thanks a lot,srdjanSrlle (srdjan),Please stick around. Not all of us sound as patronizing.L.

1. The precision of forecasts can only be assessed if you choose a loss function. This could be based on a statistical criterion (e.g. mean square error) or something economic (a hedging error). The former is easier and hence more popular.2. Realised volatility (from, say, 5-minute returns) is believed to be very accurate, unlike historical volatility (which is usually defined by daily returns). Most researchers now employ realised vols. whenever possible.3. Intraday works best. You might like to look at a paper on FX volatility forecasting by Pong and others in the Journal of Banking and Finance, 2004.4. High and low prices can be much better than closing prices, but prices every 5-minutes or so are probably better.5. GARCH is applied directly to returns, without any prefiltering.There is much more about these subjects in Taylor's Asset Price Dynamics...Good luck!SV