I've heard that IV predicts future HV. IOW if the IV is higher(lower) than the current HV, then the HV will move up(down) towards the IV. But you're saying it's actually the opposite: HV leads IV. I thought maybe there was some trend analysis applied to HV to indicate the 'true' direction of future volatility, but maybe that method isn't as common as I imagined.
The relationship between Implied and Historical Volatility is intriguing ... and got me thinking ... which is good fer me
Are you sure the historical volatility of MSFT scales as sqrt(T) between daily returns and 3-months returns ?
I'm never "sure" of anything In the spreadsheet, I download daily prices, calculate daily returns, then scale 'em up by SQRT(250) to get annualized. If I had used monthly returns, I'd scale up by SQRT(12). How would you do it?
The thing is stocks do not exactly follow a gaussian distribution. In a gaussian distribution, scaling follows a square-root function. If you compute daily returns and scale them with sqrt(250), weekly returns and scale them with sqrt(52), monthly returns and scale them with sqrt(12), you won't usually get the same annual volatility, proof (out of the statistical error) that scaling is not precisely a square root.
I don't try to predict the HV(250 days) with the IV, rather I take the HV(very long period, at least 4000 days) of an asset-class as a "fair value". Maybe you know that the P/E of any stock is 14 on the average in the long run. When the HV of single stocks is 32% on the average in the long run, why should I pay more than 32% IV?
...logb(x) ...? Edit: I guess I should ask if your referring to skew or kurtosis. I believe logarithms help cure (normalize) the skewed distribution at only a minimum cost of precision.
I successfully used the following formula: EmbeddedVolatility = Log(AbsValue(ATR/C)) Sometimes I use MA with length 7 on that
This is true - the density of stock price returns is very rarely normal - and significant differences in statistical properties are observed as one moves from smaller to larger time scales - eg autocorrelation in SpotFX prices. You might wish to look at Levy distributions - don't know if this will help in this case. Indexes are a different animal, but you'll find that some pricing models express volatility as a function of the price of the underlying, and if you wish to go to multi-factor models, then its stochastic volatility time and the real fun begins. This might be of some assitance to the mathematically minded... http://www.amazon.com/exec/obidos/t...103-4282373-6041457?v=glance&s=books&n=507846