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Richard,
After the discussion about volatility, I took the liberty of sending and
Email 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" <info@xxxx>
To:
Anthony Faragasso <ajf1111@xxxx
In the Monte Carlo probability calculators, we use trading days because
the
model is interested only in trading "units." That is, we could use
10-minute bar charts if we had the data.
In the Black-Sholes mode, and thus in implied volatility, the standard
is
to 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 that
options have 2 3/4 days of time decay
over the weekend, and if you are using Trading days, this does not take
weekends into account.
Best Wishes
Anthony
Richard Alford wrote:
> I too have lost 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>) -
> cfhttp://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. One of 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 multiplying the 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 that used trading days in its
> calculation,
> you'd need to increase the 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
> 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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