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You might say two very different animals were confused - option equivalents
and dynamic hedges.
Option equivalents, by definition, require total equality with the original
position regardless of time, price, or volatility of the underlying. In
contrast, dynamic hedges are, of necessity, fleeting approximations to an
ever-changing reality, thus needing constant readjustment. For the latter
only, delta/gamma calculus is the right tool.
Regards,
Michael Suesserott
-----Ursprungliche Nachricht-----
Von: moog@xxxxxx [mailto:moog@xxxxxx]
Gesendet: Thursday, December 14, 2000 08:44
An: realtraders@xxxxxxxxxxx
Betreff: [RT] Re: Trading Events
Excellent Mike. As regards your "this is true only within very
narrow constraints of time (at the time of purchase)" point, I would
simply add that if one wishes to remain fully hedged after buying
say, 10 ATM options and selling 500 shares of the underlying stock,
dynamic asset replication is necessary. That would typically be
conducted by buying or selling amounts of the underlying in reaction
to changes in the variable relationship you have outlined (the
results of which can never be perfect).
--- In realtraders@xxxxxxxxxxx, MikeSuesserott@xxxx wrote:
>
> 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@x...]
> 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@xxxx 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@x...]
> > 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
> >
> >
> > To unsubscribe from this group, send an email to:
> > realtraders-unsubscribe@xxxxxxxxxxx
>
>
>
> To unsubscribe from this group, send an email to:
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