Hi guys,The market standard for the realised volatility calculation of a variance swap is: Sum(ln(S(i)/S(i-1)), .i.e. the "standard deviation without the mean. In theory, is the expectation of realised vol:1- the expectation of the "standard" realised vol (as defined for a varswap) 2- the realised volatility WITH mean?

Cquand your question is relevant. Indeed the realized volatility (RV) is not the fine approximation of the volatility from theoretical point. You can construct either linear decreasing , increasing, or periodic functions having the same RV and therefore these three would be equally priced. These scenarios form "basis" of possible scenarios that are priced. If the pricing method is correct then pricing covers a combination of these 3 scenarios. If you or investors know about it is not a big problem. Instruments could hedge such scenarios. The only the notions used might be not used in their correct meaning. There are other more accurate measures could be used. See:http://www.eurexchange.com/download/doc ... oretically as far as it could be judged one took a log normal model writes a correspondent discrete approximation for sigma squared and omitted delta _t terms. Theoretically it is possible if delta_t small. In our case it is 1 day and therefore all omitted terms are meaningful and seem better hold them.

Thanks for the answer. In theory or at least in any model with prices generated in a normally distributed manner with zero mean, the expected variance predicts the realised vol with and without mean as the mean rate of return to be zero is an assumption of the model.As the market standard for any volatility prodcuts is to use the realised vol without mean, that assumption seems appropriate. However, I've seen (I'm not sure...) that correlation swap and covariance swap payoffs are defined with the mean:- Do you know the market standard?- In case of payoff with mean, it would affect the players (especially for short-term contract), as historically the covariance (resp. vol and correl) without mean realises at a premium to the covariance (resp. vol and correl.) with mean. If the instruments are priced within a zero mean framework, the short player will benefit of this "unfair" permium. Is that correct?

From numerical point of view to state that "As the market standard for any volatility products is to use the realized vol without mean, that assumption seems appropriate " one needs to calculate with mean and without mean and be convinced that the difference is insignificant though it is true for a particular mean(=trend ) behavior. From general point it could be checked if we get an estimate of the squared mean value over the interested period. If it is small then you could ignore it and realized volatility might be good. Might be if closed or open prices are reliable statistics. That also ia a question. I don't know about standards. From what it might be institutions developed instruments and correspondent documents. They then be approved regardless if mathematics used good or not very good. Then it is a problem of sale persons who do not know details at all. This is business you buy if you think you could. Similar to as you buy a car . You have money and dealers have to convince you to buy. They do not now any details and it might be better do not listen them if you have some experience. Having the paper's variance estimations for volatility it would be rather skilfully to use different for the same contract and compare results.

The expected return on the market is 4 basis points per day or 0.0004 while the standard deviation of returns is a little over 1% or say 0.0125 approximately. These numbers should convince you that it is a waste of time to subtract the mean and justify the standard practice of not doing so.

I agree that everything is consistent as varswaps are priced "without mean" and the realised vol is wihout mean too. However, the impact of this assumption could have been significant.To illustrate this, I've looked into the follwing classic strategy: Short STOXX50E varswap front month (100k starting in 2000): if the payoff of the varswap was "with mean", the strategy ends up +30mio (i.e. 3.9mio pa), wherease using the standard realised vol, it ends up +26.8mio (i.e. 3.4mio pa). Over the past 10 years, the average spread between the 1m realised vol w/o mean and with for the STOXX50E is ~0.45% (and 1Y ~0.05%).Again for varswap, everything is fine. However, I wanted to know if the pricing correl (or covar) swap is consistent with their payoff, as the difference between "with and without" mean is even more significant for correl (at least for the short term).Anyone knows if the payoff of correl swap is with or whitout mean?

Example: Yesterday Data for DJIIndex Value: 11,230.73Trade Time: Sep 9Change: Down 280.01 (2.43%)Prev Close: 11,510.74Open: 11,514.73Day's Range: 11230.73 - 11577.5052wk Range: 10,732.00 - 14,280.00it shows that market return depends on a market. 2.43 >> 4bp. If we use high and low data estimates will be different. So market return is also might depend on a method used for its calculation.

To follow up acastaldo's comment, you could also ask about subtracting off any serial autocorrelation effect. That would also be small. Sometimes these things have little impact on vol measurement but they might guide your hedging.P

To continue the subject: when we talk about return of the day from the day data we have 2.34% on the other in realized volatility exactly the same data is converted to perform volatility estimate so what is the mean? Is the expected return of an instrument for which realized volatility estimate of the mean suggests 0 is really 0?

tough question... if a stock goes up +5% everyday, the realised vol is 80% and the standard deviation is 0%. I know don't which measure is the most interesting but interestinlgy by default, Bloomberg <HVG> will show the standard deviation... I wonder if some people look at this to make their vol market

The example somewhat surrealistic. It will be look better if we have RV 3% stdv 0%. What wood be everyday change ? Note it is better to say change because we can construct a dynamics as we wish. It could be pure growth or lossl or say a period of growth and then loss.