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Please bear with me, this is going to be a bit long. I am, of course, aware
that many of you would not need any detailed explanation, least of all Ira,
but I am trying as best I can to really clarify the issues here.
Let us start with that line of reasoning from Ira's post - "ATM options have
50 deltas, therefore 10 ATM options are equivalent to 500 shares of stock".
This is true only within very narrow constraints of time (at the time of
purchase) and price (near the strike price). For two positions to be
*equivalent*, however, more is required. We would want to see them behave in
parallel during their complete life cycles, and for all possible prices of
the underlying.
The attached graph may help to make this more clear. It simply shows 10 CSCO
Jan 55 calls (blue) and the - supposedly - equivalent position of 500 shares
of this stock (red). The dashed blue line shows the behavior of the option
as of today, and the solid blue line, at the time of expiration. Please see
att1.gif.
It is immediately obvious from the graph that the "equivalence" is
restricted to a very limited area where the red line is tangent to the
dashed blue line. The farther we move away from that region either time-wise
or in price, the less the two tally. At expiration, the slopes of the two
straight lines are completely different. These two positions are not
equivalent!
Mathematically, of course, deltas correspond to first derivatives which are
local to each point of a curve; therefore, one delta value (such as 50)
cannot correctly describe the behavior of even one curve, let alone of all
of the curves arising during the life cycle of an option. Deltas do not
establish equivalence.
Let us have a look now at the second graph (att2.gif) which shows a straddle
consisting of 10 CSCO Jan 55 puts and calls each (blue position).
Superimposed in red color you see the position that was erroneously believed
to be equivalent - long 10 CSCO Jan 55 calls, short 500 shares of CSCO. Are
they equivalent? No. Please see att2.gif.
Incidentally, the slight asymmetry noticeable in this graph is due to the
strong volatility skew in this stock today.
Now, if you took 20 calls instead, and shorted 1000 shares of CSCO, you
would have perfect equivalence with the 10x10 straddle. It doesn't make much
sense to show a graph of this, because both positions, being really
equivalent now, are visually undistinguishable from each other.
Regards,
Michael Suesserott
-----Ursprungliche Nachricht-----
Von: Ira Tunik [mailto:ist@xxxxxx]
Gesendet: Monday, December 11, 2000 16:00
An: realtraders@xxxxxxxxxxx
Betreff: Re: AW: [RT] Re: Trading Events
The math appears to be 10 at the money calls or puts at 50 deltas would
would
equal 500 shares of stock of 5 futures. Long 10 puts and long 10 calls
would
make you long 50 deltas and short 50 deltas per contract and therefor long
or
short 500 shares of stock or 5 contracts. This assumes that there straddle
is
at the money and the price of the underlying is at the strike price. In
actuality, the put will always have less deltas then the calls because of
the
converstion/reversal. In my book that makes it 10 calls and 500 shares or
5
of the underlying. If there is an error here please let me know. Ira.
MikeSuesserott@xxxxxxxxxxx wrote:
> Robert,
>
> though I don't consider myself a guru of anything, I do trade options
> professionally, and I have seen this misconception come up several times
on
> this list. To clarify once again: suppose you consider a long straddle
> consisting of 10 calls and 10 puts. To make for an *equivalent* position,
> you would need to buy 20 calls and sell 10 futures contracts - not 10 and
5!
> Just do the math, and you'll see for yourself.
>
> Thus, being long 20 option contracts in both cases, you have exactly the
> same Vegas (sensitivities to volatility changes) in the central areas of
> both positions. Even the Thetas (sensitivities to time decay) are
virtually
> the same.
>
> Differences arise in the follow-up strategies, of course. Orders in the
> underlying are usually easier to handle due to better liquidity, and the
> bid/ask spread, as a rule, will be tighter. On the other hand, margin for
> the underlying is often a multiple of what you would pay for the options,
so
> if you want to hold the position for some time this would have to be taken
> into consideration, too. This is especially true for equities, where the
> money outlay can be a real drain on your capital available for trading.
>
> Regards,
>
> Michael Suesserott
>
> -----Ursprungliche Nachricht-----
> Von: Robert Hodge [mailto:r-hodge@xxxxxxxxxxxxxxx]
> Gesendet: Sunday, December 10, 2000 21:56
> An: realtraders@xxxxxxxxxxx
> Betreff: RE: [RT] Re: Trading Events
>
> Perhaps a cheaper way is to buy either the put or the call and take an
equal
> and opposite position in the relevant futures contract (eg buy a call and
> short the future). I think this would be less sensitive to any (likely)
fall
> in implied vols after the tension is released by the news coming out while
> still having the same fundamental characteristics as a straddle.
>
> Perhaps an options guru can correct me though :)
>
> Regards,
>
> Robert
>
>
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