Hi,Suppose that you have to price and hedge a one-touch option (paying one if at any time, the underlying, initially at 100, reaches 80). With a good model, you get a theoritical price which incorporates the smile. But you then need to hedge the vega, the vanna and the vomma. Suppose that you only can use vanilla options (no other exotics). You will have to estimate the cost of this hedge and add it to the price given from the model. I read some slides from Wistup but could not understand everything. So, how does it work in practice ?- First of all, what is your hedge in options ? What is usually done in practice ?- How do you account for it in your price (knowing that at the barrier, only your hedge will exist) ?If you have any papers of interest I could read, don't hesitate,Thank you

What Wystup describes is just a basic way traders assess their losses/gains if they had to hedge vega of an exotic with ATM options.It's quite ad-hoc though, and there exist many modifications of the method. One useful way of thinking of a OT option is to think of hedging it with two digital calls of the same strike. When at the barrier, they will cost roughly 1/2 each (assuming zero rates differential), as the probabilities of ending up above or below the barrier will then be equal. The digitals themselves can be ddecomposed into simple vanilla strike spreads. I do not know whether this is frequently done in practice, but I think that this way of looking at a OT helps to understand what is really affecting its price.

One touch = betBest way to hedge a one touch is with other one touches or digitals... but really one touches are best. when u start fing around with digitals vs one touch ur gonna get big duration(omega) risks. Vanillas vs digitals and one touches is also a no good hedge. u just get exposed to more and more partial derivatives.. ie: dvega/dspot, dvega/divol etc etc.... one touches also have multi signed vega functions.. (ie pos and neg for different levels of vol and S)

Thanks a lot for your answers !sgelb, I suppose that when you say "one touches also have multi signed vega functions", you mean by that dvega/dspot or dvega/svol ? That is exactly my problem with the one touch. I cannot hedge them correctly with vanillas. And, in my market, you only have access to vanillas (no IBD for digital and bets : it's a client driven activity). So, what can I do ? I think that in the FX market, bets are usually traded. Does every one hedge them with others bets like you suggest ? And what is the advantage of doing that ? I suppose that you get an exposure to the 6th moment while reducing the 4th one.

Lets say you are long an OTM one touch.You are long vega, but as vol rises, your first exit time decreases, so your real vol/vega exposure drops. So you are short up vol gamma.. see? if u bought one touch, and sold straddle, ud be hurt if vol went up. This effect is more pronounced the closer you get to the barrier.If you are short one strike, long the next etc.. your exposures are pretty balanced,.. My personal take on this is, just take a view on direction.. and trade the delta against it.

Lets say you are long an OTM one touch.You are long vega, but as vol rises, your first exit time decreases, so your real vol/vega exposure drops. So you are short up vol gamma.. see? if u bought one touch, and sold straddle, ud be hurt if vol went up. This effect is more pronounced the closer you get to the barrier.If you are short one strike, long the next etc.. your exposures are pretty balanced,.. My personal take on this is, just take a view on direction.. and trade the delta against it.

Can anyone please explain to me what's goinig on in Wystup's article?Given it's 4 pages long, the number of things in it I don't get is amazing.Part of it has to do with my unfamiliarity with hedging strategies. Why are we trying to hedge volga and vanna? What does it mean to unwind a hedge?Why does it only happen if we fail to touch the trigger?Secondly, he seems to assume that vanna of RR and volga of FLY are both zero.Doesn't work out for me. Do we compute vanna and volga simply by taking the corresponding second derivative of BS formula? Do we use ATM or implied volatility?Thanks a lot!

Where do I find the Wystup article being referred to here? Many thanks

Here.A.

Many thanks, Anton.

Out there I remember a very nice paper on barrier and one-touch options...let me find out...found...http://aleasrv.cs.unitn.it/techalea.nsf ... ortunately is in italian, but it's one of the best treatment on this topic....

Thank you Stefanone.Unfortunately, I do not clearly understand italian, even though the titles seemed interesting ! Do you know any other paper in english dealing with the subject in a similar way ?