Hi all,Just want to clarify the naming convention of barrier options. I have always considered this to be true.Binary Option = American Barrier Option (i.e. one-touch)Digital Option = European Barrier Option However, I've been challenged a few times now by people who are adamant that a the terms "Binary" and "Digital" are the same. (Including some academics)Am I going crazy or has everything been redefined?

Neither term refers to a Barrier option in my experience, they just mean that the payoff is the Heaviside step function (i.e. a fixed amount or nothing, hence the names as there are only 2 possible outcomes) and are inter-changeable.

Digital = Binary, you have either cash or nothing or asset or nothing or gap. Barriers are a whole different "beast:http://www.sitmo.com/eqcat/3 Also american/european doesn't make sense for barrier, it's american by definition otherwise it's a binary.

QuoteOriginally posted by: HansiDigital = Binary, you have either cash or nothing or asset or nothing or gap. Barriers are a whole different "beast:http://www.sitmo.com/eqcat/3 Also american/european doesn't make sense for barrier, it's american by definition otherwise it's a binary.Thanks, I was looking for opinions. Your argument is identical to that of the last person I mooted this with. I found a reference to a Binary American being the same as a One Touch. However if you look at the following, a simple American Binary is deemed to be the same as a one-touch. QuoteSource: WILMOTT P.Paul Wilmott on Quantitative Finance Volume Part I. (2nd Edition) p.1619.7 ONE-TOUCH OPTIONSWe saw the European binary option in Chapters 2 and 7. The payoff for that option is $1 if the asset is above, for a binary call, a specified level at expiry. The one-touch option is an American version of this. This contract can be exercised at any time for a fixed amount, $1QuoteSource: SuperDerivatives GlossaryTypes of binary optionsYou can create the following binary options:One Touch (ot)No Touch (nt)Double One Touch (dot)Double No Touch (dnt)One Touch with Knock Out (otk)No Touch with Knock In (ntk)http://www.sdgm.com/en/Support/Glossary ... 20overview Ultimately it's appears to be a matter of nomenclature... the maths stays the same whatever we call it.

One Touch = Barrier and is the American equivalent of binary which is by definition European.