Another Options Thread

[mazzatelli]

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?

x-axis: spot price, y-axis: superimpose gamma and theta.
Here is the plot for a long call payoff: S=100, t=30, volty=15%, r=10%, you can play with the calendar equivalent.

"][/URL]

Mathematically, approximation between the two partials:

-theta ~ 0.5 * gamma * S^2 * sigma^2

Theta is about half the magnitude of gamma.

By 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.

vi, I respectfully disagree with your interpretation of gamma, and sinner, that is a good topic to discuss but I must let Wayne have his fun!!! Less bs in his explanations too, lol.

 

[mazzatelli]

Theta is about half the magnitude of gamma, in this case.

Revised, r is assumed to be zero

 

[village idiot]

mazza

thanks once again for your reply, which as always is;-

- too short
- highly knowledgable and technical
- over my head
- makes me want to ask 3 more questions...

vi, I respectfully disagree with your interpretation of gamma

well to be fair its certainly not my interpretation of gamma, but it is my interpretation of the main risk facing someone in the specifc situation of being an a short straddle or long calendar or a butterfly, who finds himself with the underlying right at the relevant strike at a time when the 'end game' is commencing ie the payoff profile falls off sharply to either side of the current price. 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

so what should we call that? perhaps movement risk?

 

[mazzatelli]

Ha! If you can't dazzle them with brilliance, then baffle them with bullsh*t

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

There you go, couldn't have said it better myself. Apologies, I know you understand the risks, its just for pedant reasons I'm debating definitions, as new people who read it may take that interpretation of gamma.

E.g. short otm gamma - the figure would be small, initially. It would be confusing to apply the interpretation "risk of 'movement away from current price", as you are referring to atm parameters.

 

[village idiot]

yeah point taken, I guess I could have avoided some confusion by being more specific in the first place.

I had cause to consider this topic last week when i had a calendar in WOW in just the position we were talking about; i had opened a nov/dec long calendar 27.00 put spread when WOW was around $29 a while back as a cheap speculative directional play, more of an experiment than anything else really to follow how it went. As it turns out it went really well as the slow grinding movement ended up at the strike at just the right time, and it is nice to see a spread with both legs in profit on the way down.

it first crossed the strike on tuesday am which is when you suggest closing it, and I wouldnt have been too far wrong in doing so. I chose to hang on however and ended up closing it on thursday am with WOW at 27.01. That was more to do with the fact i had to go out for ther rest of the day and couldnt risk assignment than being worried about it moving away by more than the amount i was 'paying' to buy it back 4 hours early.

as it turns out i prolly didnt make too much more by hanging on (v closing when it first crossed), even though it stayed right where i wanted it, so next time i am in that position i would at least give closing as it crosses more consideration.

 

[mazzatelli]

Nice! It depends on your trading method.
E.g. Model predicts a 1stdev drop in Px, 1stdev rally in stat-vols with favorable tenor skew. Long otm put calendar and offset when forecasts are touched.

If you play delta neutral, +theta with discretionary adjustments, its reasonable to hold on, and extract as much bleed as tolerable.

Additional topic: implied vol is used to consider future realized vol. Usually the implied vol figure is taken for granted. Where does it come from? How is it calculated?
Furthermore how should we measure/calc realized vol?

Discuss.

 

[sails]

...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...:

Mazza, please feel free to translate the above into official terminology...

VI, well done on your WOW calendar...

 

[mazzatelli]

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...:

lol M, while you produce essays, I'll condense to one liners.
Back month g/v bleed > front month, closer to expiry :

Right, calendar is +theta when otm. I was referring to when the position was initially otm, touches neutrality and subsequent decision to hold or not - rather than holding an otm spread into expiry.

 

[mazzatelli]

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?

 

[wayneL]

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?

I've always thought hi-lo should be incorporated into RV calcs somehow. Never found a way to do that successfully however.

I'm all ears.

 

[sinner]

As an options noob, I did research on RV to try and understand what the hell mazza was talking about. I learned there are tricks.

There are many papers which deal with calculating RV based on tick sampling.

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.springerlink.com/content/n0hmvu8q307l773l/

6. 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.

http://www.scribd.com/doc/36871300/An-Introduction-to-Realized-Volatility

scholar.google.com is your friend.

Are the equations

(((Open-Close)*(Open-Close))/Close)*100

or

((High-Low)/Close)*100

of any use to you?

 

[village idiot]

isnt what you are talking about, what is called the 'extreme value' method as an alternative to the close to close method;


http://www.linnsoft.com/tour/volatility.htm


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

 

[village idiot]

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?

 

[sinner]

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?

Like this? P&F(High Low) 1% boxsize, 1 box reversal.

 

[village idiot]

yes, each move is exactly the same as one box on an P&F chart.
the measure of volatility is essentially how many of those boxes occur over whatever time frame is being considered.

 

[mazzatelli]

There are many papers which deal with calculating RV based on tick sampling.

Yes, as you'd know, the increase in frequency allows the sampling distribution to converge to normal. There are practical limitations: access to tick data and micro-structure affecting vol calcs if periodicity is high.

There's a lot of work developing in this topic from both an academic and practitioner's point of view.

Take the logarithmic form:
ln(high/low) or [ln(high) - ln(low)]

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

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.

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?

Looks like you are defining a distribution, but instead of conventional sigmas, you are choosing arbitrary percentages. It's similar to hedging based on fixed deltas, but I wouldn't call it a measure of vol itself.
I definitely would not use it to price securities.

 

[village idiot]

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.

thanks
we ought to call this thread the mazzatelli well; shout any question you like down it and mazzatelli shouts the answer back up...

Out of interest I've just done this chart so i might as well put it up here;

the chart shows three different measures of vol for 14 diffrent instruments, arranged in order of HV (close-close); it compares close-close HV with Hi-Lo HV, as well as the frequency of 2% moves (expressed as a percentage). All are over 250 days. Cant disagree that the 2% is arbitrary.

close-close HV and Hi-Lo HV match each other closely, except perhaps for the observation that in the lower vol instruments the Hi-Lo HV is higher than close-close, indicating there may be more intraday vol than the close-close HV is letting on in 'low vol' stocks. the correlation coefficient for these two is 0.9490 (for this particular sample)

the third bar is the measure i outlined above. the correlation between this bar and the close-close HV is actually 0.9855, which is a bummer as I was actually looking to find differences between close-close HV and frequency of useable movement...

 

[mazzatelli]

Hey vi, thanks for putting up you analysis
For equities, try comparing hi-lo to open-close...

 

[village idiot]

isnt open-close going to be the same as close-close minus any gaps?

or am I being leveled?

 

[mazzatelli]

Its because of assumptions behind hi-lo [continuous, GBM process, 24hr market] - so open-to-close is considered a more appropriate comparison.