Are Synthetic Options Truly Equivalent Options?

O

OddTrader

Quote:"The basic structure of a synthetic call option is one long put for evry one long furures contract. The futures contract underlying the put option is the same contract in which the long futures position is held.

The combined risk/reward profile is Equal to the risk/reward profile of a call option with the same contract as underlier.

The risk/reward profile refers to the risk/reward, as it will be at option experation, not during the term of the hedge.

All the comparisons in this case thus valid on the basis that all options are held to expiration.", by Stephens.

Most often, people simply say a synthetic call option is an equivalent to a call option, without adding any conditions at all.

Any comments?

http://www.elitetrader.com/vb/showthread.php?s=&postid=249410
Quote from OddTrader:

Perhaps a synthetic call is equivalent to a call, but it is Not actually a call. Right?
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Quote from MTE:

The synthetics are valid at all times not just at expiration.
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... and I wonder why people have such difficulty with this when simple arithmetic proves it?

I've often seen guys who have been options professionals say things like - "a put IS a call and a call IS a put".

One could argue the semantics, but essentially true, you are just flipping the delta via underlying, to convert one to the other.
 
Quote from OddTrader:

Quote:"The basic structure of a synthetic call option is one long put for evry one long furures contract. The futures contract underlying the put option is the same contract in which the long futures position is held.

The combined risk/reward profile is Equal to the risk/reward profile of a call option with the same contract as underlier.

The risk/reward profile refers to the risk/reward, as it will be at option experation, not during the term of the hedge.

All the comparisons in this case thus valid on the basis that all options are held to expiration.", by Stephens.

Most often, people simply say a synthetic call option is an equivalent to a call option, without adding any conditions at all.

Any comments?

http://www.elitetrader.com/vb/showthread.php?s=&postid=249410
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The quote was copied from a book "Managing Currency Risk using Financial Derivatives", by John Stephens, An IIA Risk Management Series with The Institute of Internal Auditors UK and Ireland, Published 2001 by John Wiley & Sons Ltd, page 178.

The same author has got two other titles published in the IIA series:
- Managing Commodity Risk
- Managing Interest Rate Risk.

The Series Editor: Andrew Chambers.

Do you know them well?

Why are you so sure he is wrong?

Do you have serious doubts for the publisher or the institue because both their review processes have had any proven problems in the pass, as you know for sure?

Which are the reliable publishers you think that are qualified in your view for this kind of finance or risk related books?
 
Calls and puts behave differently. Each is affected differently because of the nature of their Greeks. The biggest difference is fear vs. greed. Fear overwhelms greed; long puts gain more than short calls when volatility is high. When volatility is low, then short puts gain quicker than long calls. Just my observation. This is true even with the same amount of movement in either direction. Therefore, if I were going to do a synthetic call, I would pick an ATM put three months out rather than one that expires in the current period, for example. Lots of flexibility here. I would do the same putting together a synthetic put.
 
Quote from jwcapital:

Calls and puts behave differently. Each is affected differently because of the nature of their Greeks. The biggest difference is fear vs. greed. Fear overwhelms greed; long puts gain more than short calls when volatility is high. When volatility is low, then short puts gain quicker than long calls. Just my observation. This is true even with the same amount of movement in either direction. Therefore, if I were going to do a synthetic call, I would pick an ATM put three months out rather than one that expires in the current period, for example. Lots of flexibility here. I would do the same putting together a synthetic put.
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This is a complete red herring... What does skew have to do with put-call parity?

Put-call parity holds for European options (and American options if they're held to expiry), with some very rare exceptions (some have been alluded to by Alan; some are sometimes evident in exchange closes for far ITM/OTM options).

P.S.: There can be one important difference and that's the exchange margins. Some exchanges actually don't do the margins right, so you can gain an advantage owning a synthetic (there were some cases like that with UST futures).
 
Quote from MTE:

The synthetics are valid at all times not just at expiration.
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If that was true then there would be no rate-risk in the box market, among others.
 
Quote from jwcapital:

Calls and puts behave differently. Each is affected differently because of the nature of their Greeks. The biggest difference is fear vs. greed. Fear overwhelms greed; long puts gain more than short calls when volatility is high. When volatility is low, then short puts gain quicker than long calls. Just my observation. This is true even with the same amount of movement in either direction. Therefore, if I were going to do a synthetic call, I would pick an ATM put three months out rather than one that expires in the current period, for example. Lots of flexibility here. I would do the same putting together a synthetic put.
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Wow, this is wrong on many levels.
 
Just found: "parity and arbitrage"
http://www.elitetrader.com/vb/showthread.php?s=&threadid=165975

Quote from MasterAtWork:

Wrong.

"It can be proved under essentially the same weak assumptions that
the above put-call parity relation does not hold for American-style
options. Here is a rough outline of the proof.

Consider the case of a non-dividend paying
stock and a strictly positive interest rate.
Then, a similar arbitrage argument to the above shows that for a
european-style call option with price c, it must be true that c > max[0, S - K e^(-r T)].
Since an American-style call C is always worth at least as much, C >= c > S - K.
But if C > S - K, then the option will never be exercised, so C = c.
That is, an American call has the same value as a
Euro-style call when there are no dividends and early exercise for it is
never optimal.

But, under the same circumstances, things are quite different for the put.
An American-style put is worth strictly more than
its Euro-style counter-part. To prove it, assume otherwise. Then,
since a perpetual Euro-style put is easily shown to be worth zero,
a perpetual American-style put must be worth zero.
But this is a nonsense conclusion since an American style put must not decrease
in value as the time to expiration increases. The premise must have
been wrong, so under a no-dividend assumption, the American-style put value P is
strictly greater the Euro-style value p. Hence P > p = C - S + K e^(-r T).
In words, the American-style put value is *strictly larger* than the value given
by the put-call parity relation. For more details see:
R.C. Merton, "Theory of Rational Option Pricing",
(Bell J. of Economics and Mgt. Science, 4, 1973, 141-183.)

And,

"The relation doesn't hold for American-style options, which
allow an early exercise prior to expiration. For example, one
of the options legs in the conversion trade may disappear
prior to expiration because of an exercise/assignment. Closing
the whole trade at this point produces a gain/loss that is
unknown when the conversion is initiated.
Not closing the trade leaves a risky position. "


So, there is no call put parity for american style options.
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Quote from MasterAtWork:

You need to understand something.

A parity is composed by a call, you're right, and....a put.
So yes there is no interest to exercise an american call, but an american put.
If the put is exercised, then there is no more parity.

An another way to see that, is to consider c european call, C american call, p european put and P american put.

If there is no dividend, C=c, but P>p
So, C-P can't be the same as c-p.

But, yes I agree. It has nothing to do with the price of tea in China.
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Quote from MasterAtWork:

Try this :

Vol=30%, r=5%, spot=100, strike=100 dividend=0, maturity=365 days

American call = 14.231
American put= 9.861
European call=14.231
European put=9.354


Hence one can't have at the same time
American call-american put=european call-european put= call/ put parity
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