If it's the way you understand the point... My point was easy to grasp: there is no way to replicate a vanilla with CON only, and trying to replicate a vanilla with AON and CON is foolish. Maybe you can show us how to replicate a VANILLA with CON ? Do you ? Well if you couldn't You may try to show us your pricing model without assumption that would match market prices http://www.elitetrader.com/vb/showthread.php?s=&threadid=201844&perpage=6&pagenumber=12
What is wrong with example I gave earlier in this thread (bet1 and bet2 description). Notice that payoff is such that it is determined at end of time horizon (european). It is not the first time that this question and related clarifications have been made in this thread. What does your question have to do with what was written so far? It is missing the asset or nothing option, in addition to other specifications.
UBS, Oanda, formerly SocGen(clickoptions), JPM equities and others. I've traded European digitals/binaries, European range and synthetics, American range (DNTs), touches, and lookbacks.
I think I understand what you are saying, but your communication skills are...um...lacking. You are basically asking if the payoff goes to $1 at the moment the underlying crosses the threshold (American), or if the underlying must be above the threshold at a agreed upon time to get paid that $1 (European). (The American binary topic results an interesting thought process..it reminds me of the ITM call exercise for a dividend play modeling process--its a very binary type of decision.) If the above is your definition of American binary, it would make pricing "American" cash binaries very difficult. European binaries should be very simple to price, as long as there is a vanilla option chain from which to reverse crunch the underlying's future distribution. Regardless, you can't replicate the vanilla options risk exactly using binaries, nor vice versa. That doesn't mean that you can't trade them in the same portfolio and use them as rough hedges for one another. I have read through this entire thread. It is boardering on an interesting discussion but there is no actual topic here. Do you have an issue that you would like to brainstorm through? Or do you have a statement that you are trying to discuss.
Using the European style as you described it, why do you think your statement is true? Note that binaries include both cash-or-nothing binaries and asset-or-nothing binaries (in the latter case one gets paid with stock paper and not with cash paper) . My impression is that you may be thinking in terms of cash-or-nothing binary options ONLY when you wrote the above statement.
Thanks. With regard to European digitals/binaries, is buying them when ATM short total volatility with limited risk and a more than 2 to 1 maximum reward/risk ratio? If correct how do they compare if strike is not ATM particularly when it is OTM (for instance could theta change signs?). If you can share few words on how you use them it would be helpful, but it is understandable if you prefer to keep trade secrets a secret as you should.
ATM euro-ex digital at 2:1 reward? Never. By definition it's an even money prop. Digitals don't flip modality on greeks. I may be missing your questions. ATM euro digital bets are priced anywhere from 52/100 to 60/100 depending on dealer.