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Jeff,
many people have this notion - that as soon as a stock is involved in
replicating option positions, the result cannot be precisely the same. Their
reasoning goes more or less like this: options are subject to time decay,
and react strongly to volatility changes; stocks, on the other hand, are
subject to neither of these influences, so there just has to be a
difference. Well, this is but another common misconception.
Suppose with JDSU at 60, we bought 10 JDSU Mar 60 calls and simultaneously
sold 10 JDSU Mar 60 puts. This is called a "synthetic long". Slippage and
brief imbalances aside, this position will behave *exactly* as if we had
bought 1000 shares of JDSU. What about time decay? What if volatility rises
or falls? No effect. The option position will still behave like the 1000
shares of stock - if JDSU rises by 1 point, you profit by $ 1000 from the
options, and vice versa if it falls.
Here is how it works. The effects of time decay and volatility changes in
these two options neutralize each other. And why do they? There is a deep
reason for this. The mathematics are a bit involved, so I'll only address
one important aspect here. Stocks, puts, and calls are subject to one
fundamental law: the price difference between the Mar 60 call and the Mar 60
put will always equal the price difference between 60 (the strike) and the
stock price at that moment. If they get out of line even briefly, a floor
trader can immediately take a riskless profit by arbitraging them back into
line. Since time decay and volatility reflect in the option prices, these
influences cannot but indirectly obey that same law.
Incidentally, in crash situations you can see this law at work in a
surprising manner. When everyone is extremely bearish we would expect puts
to be very expensive, and calls to be very cheap, wouldn't we? After all,
the last thing we would look to hedge against in such a situation would be a
rally! And yet, call prices go up to the same extremes as puts, because the
above law is still valid.
Through the workings of the same law, a 10x10 straddle can be *precisely*
replicated with 20 calls and short 1000 shares (synthetic straddle), as I
have tried to point out in a previous post. This is not a question of
"adjusting" or "dynamically hedging" anything - as long as you want that
straddle on, you might as well hold the 20 calls / 1000 shares synthetic
straddle instead; it will behave in *exactly* the same way, because the two
are equivalent.
In contrast, "hedging" always means "changing" a position, in such a way
that they are no longer equivalent. Once you see fit, in the course of your
trading, to do this, you would go into delta/gamma considerations as to how
to best accomplish it. And after having changed the position, you might
*then* say you have "adjusted" or "hedged" the original straddle, synthetic
or not.
Hope this helps.
Regards,
Michael Suesserott
-----Ursprungliche Nachricht-----
Von: moog@xxxxxx [mailto:moog@xxxxxx]
Gesendet: Friday, December 15, 2000 13:22
An: realtraders@xxxxxxxxxxx
Betreff: [RT] Re: Trading Events
Mike, as I understand it, derivatives such as options find their
precise equivalents (or can only be precisely hedged) by other
derivatives, and stock by stock...the derivatives and the stocks are
the different animals...correct me if I have this wrong.
JeffR
--- In realtraders@xxxxxxxxxxx, MikeSuesserott@xxxx wrote:
>
> 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@xxxx [mailto:moog@x...]
> 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:
> > realtraders-unsubscribe@xxxxxxxxxxx
>
>
>
> To unsubscribe from this group, send an email to:
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