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Interesting, however, I suspect he is answered the
wrong question.
In the BS methods, indeed the time used inthe
equations for the time to expiration is in calendar days. No question about
that in my mind, nor in the calculations I routinely perform. Hence
your observation that the price decreasing over the weekend more than over night
may be a partial result of that, although I still expect the floor trader's
hedge against more weekend "event-risk would have more influence, certainlyfor
longer term options where the theta-decay is very minimal. The floor
risk-adjustment show up in implied volatility calculations, and I suspect they
swamp the theta-decay of 3-days vs. 1-day. Easily calculated if one is of
the mind.
Calculation of the Historical Volatility, the topic
of this discussion, is quite another matter. An easy check is to do the
calculations yourself and compare to McMillan's values he posts. I am
fairly confident you did not ask McMillan specifically about the historical
volatility calculations ... Another check is to compare the implied
volatilities that can be back-calculated in the BS model and compare to the
historical volatilities. In either case, my experience and calculations
indicate that using bars in the stddev normalization is the more
appropriate. Difference between using sqrt of 260 vs. 365 is roughly
20% and the comparisons above are generally within that range.
Another question to ask yourself, is givena time
series with constant volatility, how would you normalize the calculations
such that calculations on shorter subsets of the data would extrapolate to the
same calculation over a year .... although this may be too degenerate a case to
be convincing. I doubt if you would use 365 bars, but rather 260 and the
full year calculations would not require extrapolation.
Anthony, my intention is not to "win this"or to
harangue you. I have worked options and the associated math for several
years and feel fairly confident in this answer based upon calculation historical
volatilities by numerous conditions and numerous variations. If one is
only interested in the changes in volatility the scale factor doesn't
matter. If you are doing BS modeling yourself, it makes a large
difference.
Best wishes,
Richard
<BLOCKQUOTE
>
----- Original Message -----
<DIV
>From:
Anthony Faragasso
To: <A title=amibroker@xxxxxxxxxx
href="">amibroker@xxxxxxxxxxxxxxx
Sent: Tuesday, April 30, 2002 3:50
PM
Subject: Re: [amibroker] Measure stocks'
volatility[response from McMillan]
Richard,After the discussion about volatility,I
took the liberty of sending andEmail to Larry McMillan concerning Calendar
Days versus Trading Days:His response is
below./**************************************************/
Date: Tue, 30 Apr 2002 15:28:53
-0400 From:
"Lawrence G. McMillan" <<A
href="">info@xxxx>
To: Anthony Faragasso
<ajf1111@xxxxIn the Monte Carlo probability calculators, we
use trading days becausethemodel is interested only in trading
"units." That is, we could use10-minute bar charts if we had the
data.In the Black-Sholes mode, and thus in implied volatility, the
standardisto use calendar
days./***********************************************************/The
second paragraph, confirms my own use of Calendar Days.As for my
comment " in the real world" , I was refering to the fact thatoptionshave
2 3/4 days of time decayover the weekend, and if you are using Trading
days, this does not takeweekends into account.Best
WishesAnthonyRichard Alford wrote:> I too havelost
enough money in options to speak with some validity> :) I compare my
calculations with those from McMillan's site, the> unquestioned guru of
options (questioning that statement forfeits you> right to speak about
options <go>) -> cf<A
href="">http://www.optionstrategist.com/free/analysis/data/index.html.His>
20-day historical volatility for, say, INTC on 4/19 is 40% - the>
sqrt(260) yields 41.2% in AB whereas the 365 would yields 48.6%.
(BTW> your 256 number you mention actually matches his the best at
40.2% -> although it is unclear how you arrive at that number - I may
change to> 256). Your observations on the option variations over the
weekend> strike me as irrelevant considering that the price is a
function of> the implied volatility - which is a function of the model
used etc.> Typically the implied volatility is much closer to the
20-day> volatility than the 20% discrepancy introduced by using 365. It
is too> late to delve into the latter points you claim. Note
that> normalization typically is a non-dimensional process and if
you> measure bars you should normalize bars, at least IMHO. Feel free
to> use whatever you choose. I will go with the numbers that
match> McMillan. Sorry to get you torqued off :) I do
wonder what you think> option pricing has to do with the real world -
but lets save that for> another day. Cheers,
Richard>> ----- Original Message
-----> From: Anthony
Faragasso> To:
amibroker@xxxxxxxxxxxxxxx> Sent: Sunday,
April 28, 2002 9:24 PM> Subject: Re:
[amibroker] Measure a stocks' volatility
with> AB
?>
Richard,>> Since I also deal alot
with Options, Here is my reason for>
using>
sqrt(365).>> Should you use 365 (
the number of calendar days ) or 256 (>
the number> of trading days), I believe
there is no absolutely correct> answer. I
use> 365 mainly for consistency. Oneof
the key functions in an>
option's> price is time ( t). The time
component is expressed in terms>
of> fractions of a year and is
universally thought of as>
Sqrt(calendar> days/365) as opposed to
Sqrt(trading days / 256).>> This
365 day calendar effect can be best demonstrated
by> looking at
the> price behavior of an option from
Friday afternoon to Monday> morning.
All> other things being equal, the
option's price will drop more> from
Friday> afternoon to Monday morning than
it would from Thursday> afternoon
to> Friday Morning. That's because
you have about 2 3/4 days of> time
decay> of 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,
I> use 365, the number of calendar days.
If you use 256, the> options
price> decline would be smooth every
trading day, no matter how> many
calendar> days transpired between trading
periods.>> There is an even more
troubling problem when you use the>
number of> trading days, and that has to
do with an assets expected>
rate-of-return> and risk over the course
of a year. The formula for> volatility is
the> annualized daily standard deviation.
Recall that you>
calculate> volatility by multiplyingthe
standard deviation figure by> the
square> root of the number of periods in
a year. If you use 256(> now)
because> that is the number of trading
days in a year, that means> you'll have
to> use some other number when the number
of trading days per> year
is> modified. That means adding
trading days would increase>
volatility,> eliminating trading days
would decrease volatility. Trouble> is,
changing> the available trading periods
has already happened several> times,
and> the real world results refute this
notion.>> Prior to 1952 the stock
market traded on Saturdays. That> meant
that> there were more than 300 trading
days per year, instead of> the
current> 256. When the NYSE made the
change in 1952, did market risk> shrink ?
No.> Did market returns shrink? No. Would
diminished returns even> be
a> logical expectation? No. Because
volatility is a measure of> risk
and> reward, however, that is what should
have happened based on> a
reduction> in the number of available
trading days. Not only are those>
conclusions> illogical, 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>
days> previously would require that you
use a larger number now> for
certain> assets ( like stock index
futures traded on Globex). If you> used
a> volatility calculation model thatused
trading days in its>
calculation,> you'd need to increasethe
number of trading days to the>
appropriate> amount. With the
standard deviation component constant,>
volatility> would have to increase due to
the increased number of> trading
periods.>> Some might argue that
volatility would remain constant, even>
with the> increasing and decreasing
trading periods. If that is true> and you
use> trading days to annualize
volatility, increasing the number> of
trading> days would imply a smaller daily
standard deviation figure.> But
does> increasing your sample size ( which
you are effectively> doing
by> increasing the number of trading
days) imply a reduction in> the
standard> deviation? Of course
not.>> It doesn't even make
intuitive sense, and is not supported> by
empirical> data. Taken a step
further, assuming that volatility>
remains constant> while increasing the
number of available trading days means>
that> investors' reactions to news and
events should result in> smaller
price> moves. For example, lets say that
a stock goes from $10 to> $12.
A> smaller standard deviation of the
price change means that> the
price> change must be smaller. So the
constant volatility premise> means
that> investors are currently valuing the
stock at an artificially> high
price> of 12 instead of correctly valuing
it at a lower price,> simply
because> the markets are currently closed
on weekends. That is> wrong. The
stock> is priced at 12 because the
information about the stock that>
is> currently available warrants a price
of 12. Saying that> volatiltiy
would> remain constant when the number of
trading days changes> implies that
the> market is currently irrational and
inefficient due to the> absence
of> weekend
trading.>> Since I believe neither
256 nor 365 is perfect , and because> I
wish to> be consistent with the way
options behave in the real world> ( that
is to> emulate the time deterioration
over the weekend) I use 365> days in
my> option models and my volatility
calculations. :-]]>> Best
wishes>
Anthony>>>> Richard
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> openit
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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