Hi everybody,Does anybody knows a closed analytical formulae to price a worst of option with barrier? For example, a worst of up and out call: if anytime during the life of the option the barrier of any of the names has been touched the option expires worthless but if it doesn't happen the payoff wil be the max ( final value of the name of worst performing - strike of this name ; 0 ). Can anybody help me? I searched on the web for an article but I couldn't find anything that could help me.Tks a lot

I always do these by FDM because they can be sensitive to correlation and I like to play around with various correlation models. These sort of contracts are very big in South Korea.P

I'm sorry but what is FDM?What are the models available to price this kind of option?

Finite Difference Method. There's a lot of be said for modeling this type of an instrument in more detail than closed form solution would give. Different corr models are Paul mentioned. Different skew parameters etc.

FDM is very suited to barriers. For example, in contrast to plain options there's no numerical boundary conditions needed. And FDM approach is valid for a range of problems. So only one solution needs to be produced. And it tends to be robust over a wide range of parameters.

FDM will be perfect as long as the dimension is small, isn't it?With stochastic correlation models, the dimension increases very quickly (2 underlyings->3 dimensions, 3 underlyings -> 6 dimensions)Some questions about stochastic correlation models:1. To calibrate those models, will you try to reprice basket options?2. Do you know some model name that could be useful for Worst Of? Smae thing for stochastic Skew model...Cheers

QuoteOriginally posted by: LapinFDM will be perfect as long as the dimension is small, isn't it?With stochastic correlation models, the dimension increases very quickly (2 underlyings->3 dimensions, 3 underlyings -> 6 dimensions)Of course, for such options yes. I wonder how you would solve a 6 PDE in FDM???? not with the current techniques.

I like Monte Carlo...

QuoteOriginally posted by: CuchulainnQuoteOriginally posted by: LapinFDM will be perfect as long as the dimension is small, isn't it?With stochastic correlation models, the dimension increases very quickly (2 underlyings->3 dimensions, 3 underlyings -> 6 dimensions)Of course, for such options yes. I wonder how you would solve a 6 PDE in FDM???? not with the current techniques.I think it's worth stopping for a moment and thinking how good such models are before you solve them.Ok, I've stopped and thought...they are stupid models. I've said this before, and will keep saying it until people start using sensible models: I do expert witness work, and will happily stand up against anyone in court to explain why such models are naive despite their 'sophistication.' They are dangerous. You are going to lose a lot of money if you use them.P

Hi Paul... Thanks for the feedback.I do agree these models are not the best, but it seems to be mkt standard.If you work on the buy side and you want to quantify the margins taken by the banks you need to use the same weapons, isn't it?On the hedge fund part, this is another story...Which kind of model you would suggest for these kind of problems while being clever?Regards

1. It is also market standard for each bank to lose $10bn.2. Why do you care how much the sell side is making? That's just 'envy.' You don't ask this question when you buy a car. (Anyway, the answer seems to often be negative.)3. Buy side is easier, you just take a chance, that's the name of the game. On the sell side it has become de rigeur to calibrate models to vanillas. 'De rigeur' but misunderstood and dangerous.4. What model to use? When we started the CQF our goal was to teach people to think and to be able to build their own models. I do not spoonfeed!P

1. True2. Envy has no part in there. I am just dealing with deception. If I find a market opportunity, I know what is my fair price under my own assumption (and so model), but I wish to know sell side price before asking for it in order to maximize my profit.3. Agreed4. Fair enough. Just asking in case....

2. All you have to do is find the person willing to sell you the contract for the least amount! If they are still making lots of money good for them!P