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
... 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.
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?
The author is simply referring to the fact that put-call parity doesn't necessarily hold for American options. That's why he's specifying the "at expiration" constraint (put-call parity holds for American options if they're held to expiry). If you want to read more about the put-call parity read the most EXCELLENT commentary by Alan Lewis in this Wilmott thread: http://www.wilmott.com/messageview.cfm?catid=19&threadid=4301
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.
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).