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all cheering aside....
Of course the Black Scholes model is basedon
Gaussian distributions, thus the sqrt(t), not t^1/4 as your apparent
typo indicates, extrapolates time variation. If you only want tosee
variation in stock volatility - forget all this stuff and simply plot Bollinger
Bands and move on; perhaps even better look at the MA(ATR()) - certainly easier
for most to consume and digest.
OTH, if you are working options and using the
BS model, which actually does a remarkable job of modeling option pricing, it is
very useful to use the numbers that the price makers use. Comparing the
20-day historical volatility to the implied volatility for options is enough to
convince one that the BS is useful, albeit modified by the floor action - the
like reason for Anthony's observation that options drop over the weekend - there
is more risk for a weekend "event" than an overnight "event", hence the price
makers build in risk premium.
I certainly know which I use and how and why I use
it; hopefully, people using other's answers test them against a known or
desired result to determine if they meet their needs, remember that "sometimes
you DO get what you paid for." :)
Cheers,
Richard
btw, Waz - I like you thought about collecting
indicator values at buy/sell points. I have been muddling with that
idea for sometime but never crystallized is as nicely as you did. One
problem is that one likely needs to define a universe, and there is always the
risk of tuning the results. Of course, that pitfall exists from any
inverse modeling system whenever you extend the domains. Still a great
idea to refine understanding of which parameters are important.
<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
Listes
trading
To: <A title=amibroker@xxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Monday, April 29, 2002 7:04
AM
Subject: RE: [amibroker] Measure a
stocks' volatility with AB ?
<FONT face=Verdana color=#800000
size=2>The use of 260 or 365 for computing annualised volatility supposes that
the stock follow a gaussian random walk, that is daily returns are
scaling like time power 0.5 (t^1/2). In fact, the statistical laws followed by
stocks are quite more complicated and the ones proposed by scientists (Levy
stable laws, GARCH models, fractal brownian motion,...) are very difficult to
use (most of them do not have analytical solutions). The problem of the
gaussian random walk is that it undervalues the risk and that is a major
problem for option valuation.
<FONT face=Verdana color=#800000
size=2>This is to say that using 260 or 365 days to estimate volatilityis not
a major issue. Imagine a stock scaling with a t^0.7 scaling law instead of
0.5, the error on the estimation of the volatility is quite
dramatic!
<FONT face=Verdana color=#800000
size=2>Just stick to one of it, 260 or 365, to be able to compare stocks,
keeping in mind that the underlying model is not very
accurate.
<FONT face=Verdana color=#800000
size=2>
<FONT face=Verdana color=#800000
size=2>Waz
<FONT face=Tahoma
size=2>-----Original Message-----From: Anthony Faragasso
[mailto:ajf1111@xxxx]Sent: lundi 29 avril 2002
04:24To: amibroker@xxxxxxxxxxxxxxxSubject: Re:
[amibroker] Measure a stocks' volatility with AB
?Richard,Since I also deal alot with
Options, Here is my reason for usingsqrt(365).Should you use 365
( the number of calendar days ) or 256 ( the numberof trading days), I
believe there is no absolutely correct answer. I use365 mainly for
consistency. One of the key functions in an option'sprice is time (t).
The time component is expressed in terms offractions of a year and is
universally thought of as Sqrt(calendardays/365) as opposed to
Sqrt(trading days / 256).This 365 day calendar effect can be best
demonstrated by looking at theprice behavior of an option from Friday
afternoon to Monday morning. Allother things being equal, the option's
price will drop more from Fridayafternoon to Monday morning than it
would from Thursday afternoon toFriday Morning. That's because you
have about 2 3/4 days of time decayof the weekend instead of the usual
3/4 day of decay during the week.Just to be consistent with the way
options behave in the real world, Iuse 365, the number of calendar
days. If you use 256, the options pricedecline would be smooth every
trading day, no matter how many calendardays transpired between trading
periods.There is an even more troubling problem when you use the
number oftrading days, and that has to do with an assets expected
rate-of-returnand risk over the course of a year. The formula for
volatility is theannualized daily standard deviation. Recall that you
calculatevolatility by multiplying the standard deviation figure bythe
squareroot of the number of periods in a year. If you use 256( now)
becausethat is the number of trading days in a year, that means you'll
have touse some other number when the number of trading days per year
ismodified. That means adding trading days would increase
volatility,eliminating trading days would decrease volatility. Trouble
is, changingthe available trading periods has already happened several
times, andthe real world results refute this notion.Prior to
1952 the stock market traded on Saturdays. That meant thatthere were
more than 300 trading days per year, instead of the current256. When the
NYSE made the change in 1952, did market risk shrink ? No.Did market
returns shrink? No. Would diminished returns even be alogical
expectation? No. Because volatility is a measure of risk andreward,
however, that is what should have happened based on a reductionin the
number of available trading days. Not only are those
conclusionsillogical, they're not supported by actual
events.Another example is the proliferation of overseas and 24-hour
trading.Based on the increasing number of trading periods, using 256
dayspreviously would require that you use a larger number now for
certainassets ( like stock index futures traded on Globex). If you used
avolatility calculation model that used trading days in its
calculation,you'd need to increase the number of trading days to the
appropriateamount. With the standard deviation component constant,
volatilitywould have to increase due to the increased number of trading
periods.Some might argue that volatility would remain constant,even
with theincreasing and decreasing trading periods. If that is true and
you usetrading days to annualize volatility, increasing the number of
tradingdays would imply a smaller daily standard deviation figure. But
doesincreasing your sample size ( which you are effectively doing
byincreasing the number of trading days) imply a reduction in the
standarddeviation? Of course not.It doesn't even make intuitive
sense, and is not supported by empiricaldata. Taken a step
further, assuming that volatility remains constantwhile increasing the
number of available trading days means thatinvestors' reactions to news
and events should result in smaller pricemoves. For example, lets say
that a stock goes from $10 to $12. Asmaller standard deviation of the
price change means that the pricechange must be smaller. So the constant
volatility premise means thatinvestors are currently valuing the stock
at an artificially high priceof 12 instead of correctly valuing it at a
lower price, simply becausethe markets are currently closed on
weekends. That is wrong. The stockis priced at 12 because the
information about the stock that iscurrently available warrants a price
of 12. Saying that volatiltiy wouldremain constant when the number of
trading days changes implies that themarket is currently irrationaland
inefficient due to the absence ofweekend trading.Since I believe
neither 256 nor 365 is perfect , and because I wish tobe consistentwith
the way options behave in the real world ( that is toemulate the time
deterioration over the weekend) I use 365 days in myoption models and my
volatility calculations. :-]]Best
wishesAnthonyRichard Alford wrote:> Anthony,
I suspect you should use sqrt(260), the common number of> bars/year,
instead of sqrt(365). The result will agree with published>
results, for instance on McMillan's site. I took the liberty of>
attaching the indicator I use if you have the nerve to open it with>
all the virus running around.> Cheers, Richard ----- Original Message
----->> From: Anthony
Faragasso> To:
amibroker@xxxxxxxxxxxxxxx> Sent:
Sunday, April 28, 2002 6:49 PM>
Subject: Re: [amibroker] Measure a stocks' volatility
with> AB
?> Hello,
Derek,>> I don't know if this is
what your are looking for, but this> is
what I> use for
volatility:>> pds=20;//Set your
time period> Graph0 =
StDev(log(C/Ref(C,-1)),pds)*sqrt(365)*100;>>
Anthony>>>>
dereklebrun wrote:>> >
Hi is there any technical analysis way to measure
a> stock's
price> > volatility in AB
?> > If yes, how
?>
>> >
Thanks,> >
Derek>
>>
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