Only trouble is I am not seeing any indication that gamma outweighs theta using this method. am i doing it wrong, or perhaps you are meaning spreads that start further out in time?
-theta ~ 0.5 * gamma * S^2 * sigma^2By gamma risk I suppose we are really referring to a risk of 'movement away from current price'
Perhaps this difference would be a good topic to discuss? I am certainly interested to learn about it.
Theta is about half the magnitude of gamma, in this case.
vi, I respectfully disagree with your interpretation of gamma
That gamma is high in these situations obv exacerbates the change that can happen in his portfolio quickly, but to call a spade a spade he just doesnt want a sharp move either way, gamma or no gamma
...If you play delta neutral, +theta with discretionary adjustments, its reasonable to hold on, and extract as much bleed as tolerable...
While testing calendars some time ago now, I found it doesn't always pay to hold on to OTM calendars close to expiry due to extrinsic value falling faster in the back month than the front (theta turns negative in the position). Just something to keep an eye on. Unless the crystal ball is working well and the market looks certain to come to your strike at expiry, then hold on...:
Furthermore how should we measure/calc realized vol?
Not flogging a dead horse, but will spew verbatim before I'm off on a loooong holiday :bananasmi
Normally, close-to-close estimation is the calc for realized vol, however there could [up to you to research] be a measurement error - i.e. it is not an accurate measure of RV.
Any volty analysis could be leading to incorrect conclusions by comparing to a misleading RV.
Similar thinking applies to iv.
Any thoughts?
http://www.springerlink.com/content/n0hmvu8q307l773l/Central limit theorem for the realized volatility based on tick time sampling
Masaaki Fukasawa
A central limit theorem for the realized volatility estimator of the integrated volatility based on a specific random sampling scheme is proved, where prices are sampled with every ‘continued price change’ in bid or ask quotation data. The estimator is shown to be robust to market microstructure noise induced by price discreteness and bid–ask spreads. More general sampling schemes also are treated in case that the price process is a diffusion.
http://www.scribd.com/doc/36871300/An-Introduction-to-Realized-Volatility6. CONCLUSION In this paper we reviewedthe concept of realized volatility and correlation. We investigated the behaviour of daily volatility estimators as advocated by Bollen and Inder (2002) and Andersen et al.(2001b). In particular, by taking the study by Andersen et al. (2001b) as reference, we established that their findings also hold true for JSE stocks. The distribution of the daily returns for all the realized volatility estimators, standardized by the daily volatility estimates, is nearly Gaussian, and so is the distribution of the log of the daily volatility estimates. This is generally true for all the shares considered. The finding that daily standardized returns are normally distributed can give new impetus for the application of classic mean variance analysis. We also show that the realized volatility estimators differ fundamentally from the GARCH type estimates of daily volatility. To clarify the relation between the GARCH approach and the realized volatility approach to volatility measurement, we conducted further research which is reported in Venter et al. (2006). This paper points out that a traditional GARCH type estimator may be thought of as a measure ofex pec ted daily volatility given past information and introduces a new type of GARCH volatility called the actual daily volatility, which is quite close to the realized volatility.
and since you raise the subject i am going to throw this out for comment;
seems to me all traditional methods of measuring volatility concentrate on measuring the change (close to close), or range (hi-lo) , over a fixed period (most commonly one day).
a variant I have been working on in a spreadsheet turns it round and fixes the movement rather than the period; it attempts to measure how often a fixed movement occurs over some longer period. Suppose we fix a target movement at say 1% (so 2 targets , +1% and -1%). each time there is a 1% movement, up or down, 2 new targets are set @ +- 1%. we use highs and lows to determine each day whether a target movement has been hit, so closes are irrelevant. the targets remain the same until one is hit ie they dont move on a daily basis. so it captures intraday movemnts as well as cumlative smaller movemnts if they add up to a larger one but not otherwise
the result is a number of x% movements per y trading days figure, which corresponds to the number of adjustments you would make if using a delta hedging strategy, adjusting every x%, which is what you want to know a lot of the time
anyone see any merit in this approach?
There are many papers which deal with calculating RV based on tick sampling.
dunno where the .601 comes from but this formula does seem to make the number spat out by the extreme value method closely match the traditional method
the result is a number of x% movements per y trading days figure, which corresponds to the number of adjustments you would make if using a delta hedging strategy, adjusting every x%, which is what you want to know a lot of the time
anyone see any merit in this approach?
Yes.
The 0.601 comes from sqrt(1/4ln2).
If vol is not driven by large intra-day changes, then the two measurements are similar.
However if hi-lo vol=50% and close-to-close=25%, then close to close under-represents true vol. This has an effect on delta adjustments.
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