Hi, today I was quoting couple of banks for an European Kock-out Barrier with a rebate on an Equity Index (Ibovespa)When I got some prices back I thought their bids were too low and started to look on individual Vols and check their assumptions.The lower bid "explanation" comes from the fact that the model used was a local vol model, the vol implied in the price ~13%The surface shows something close to 20%-21%My question is, does it make sense to use the local model or not? Because the European KO is simply a callspread - a digital.Thanks

A barrier option is not a simple callspread / digital - unless I am missing sth here. However a callspread / digital can be used as an upper bound, which is maybe why you think the prices are too low. I very much doubt banks would price barrier options systematically too cheap.

QuoteOriginally posted by: outrunEuropean KO options shouldn't be called 'barrier options' imo, they only ever look at the barrier at expiration. Perhaps there is mixup wrt the underlying (spot vs futures)? ..or a mixup between American/European style?Aside from the minor question about the Kock-out barrier (?!), I am pretty sure the reference is to a European option with a continuous (American, if you want) barrier. Otherwise, I agree.

QuoteOriginally posted by: frolloosA barrier option is not a simple callspread / digital - unless I am missing sth here. However a callspread / digital can be used as an upper bound, which is maybe why you think the prices are too low. I very much doubt banks would price barrier options systematically too cheap.Maybe I'm not saying it right, I meant barrier monitoring @maturity sorry about the "European Kock-out Barrier"

In case of a single look, we usually refer to the product as a digital option rather than a barrier.

QuoteOriginally posted by: bearishIn case of a single look, we usually refer to the product as a digital option rather than a barrier.I see, thanks. Nevertheless, the payoff would be exactly the same as a call spread - digital, correct? Regarding my initial question, does it make sense to price it under the local vol?

Now that we are clear it is a "plain" digital, you can use whatever model you want to price it, but all models should give the same price for the digital if calibrated to the smile since the digital can be replicated by a tight call spread which can be observed directly. Question remains where did you get the 13% and 21% from?

Well, I'm still trying to figure it out. If you go on bloomberg and price it as a local vol you would get Black-Scholes Implied Vol of ~14% then if you changed it for the Black-Scholes of Finite Differences for the BS equation you would get a much higher implied Vol.

You have to be careful defining implied vol when it concerns Digitals. I suspect the 13% is the flat 21%vol adjusted for the skew, and BBG calls this "local vol". And if it's not that then build your own pricer - I dont trust BBG. But rellay the price of the digital is just the price of the tight call spread.Maybe this helps.

QuoteOriginally posted by: outrunI'm worried about the bigger picture, I would tell management something like this: * bank will make an easy profit on you (your company), you have no understanding what type of contract your trying to buy, how to price it,.. nor what you're letting yourself in with. * Second: you shouldn't be buying highly unstable exotic options with event driven payoff. How can a discontinuous derivative like this possibly be some sort of risk reducing factor? It'll be more like a risk *adding* bet I expect. What are the motives behind wanting take on such a position?Always nice to have a feedback like that, specially in the student forum, but thanks anyway. Regarding the payoff please don't be that confuse because it doesn't mean I don't know what I quote because I wrote it wrong here in the forum(my bad but I told above). My question is specifically regarding the price which in that case you are correct.Since I'm working on the structures desk I don't need to "manufacture" the derivative so it's not my job description to hedge the exposure all I care about is how the price looks vis-a-vis the Real World Investors expectations not the risk-neutral one. For instance, given the high level of interest rates and dividend protected or FX options it's really cheap to buy ATMs puts for 6m to 1y, even if in Volatility terms it might look like an easy profit for the counterpart. The motivation is pretty simple: We need to structure something to fit under our strategist view on the local equity index. I'll be happy to share if you more details and market conditions and see what other alternatives do we have.

If you had a competent risk manager reading your post, here are a couple of items they might want to ponder:"it's not my job description to hedge the exposure" - pricing without regard for hedging is bad in general and especially so for unhedgeable products like binaries"all I care about is how the price looks vis-a-vis the Real World Investors expectations not the risk-neutral one" - it is unclear whether you are displaying your own ignorance or merely projecting ignorance upon your customers, but somebody is clearly assumed to be dumb in this context"it's really cheap to buy ATMs puts for 6m to 1y, even if in Volatility terms it might look like an easy profit for the counterpart" - at a transaction level, derivatives trades are zero-sum games (before transaction costs), so an easy profit for the counterpart is probably not what you are looking for In all fairness, you just sound like a derivatives structurer/marketer.