Dear allfor risk management purposes I need to set up my system to price exotic fx options (binary, barrier, lookback, asian, one-touch). I cannot find quoted volatilities for these options on Bloomberg or Reuters though and I suppose I will need to use the vanilla volatility surface. What would be your suggestions as to how to use and possibly transform this surface to get most appropriate prices?I will appreciate all help.Best regards - Dunbar

once you calibrate the surface with vanillas via local vol or stochastic vol, you should be able to use it for exoticsare you asking which vanillas to use? that depends on the exotic ...

Thank you reza.I understand that in order to set up a volatility surface for eg. average rate options I need to:- calculate the local volatility surface from implied/quoted vanilla volatilities- build a tree or run a simulation using the local volatilities to get option prices- calculate implied volatilities from the prices obtained numerically.The same would apply to barrier and lookback options.Are there any shortcuts for these standard exotics?If there are not, are Jim Gatheral's lecture notes the ultimate source for local volatility calculation? I still haven't understood how the time-strike surface is transformed into a time-price one...I will be grateful for any further hints.Best regards - Dunbar

I think Espen Haug (Collector) has an article on Asian Volaitility in Issue 4 of WILMOTT Magazine

Hi,I would say that you can make your life much easier if you just stick to the vanilla vols. Especially when the vanilla vol surface is rather flat, going through local vols doesn't add anything but trouble. Asian options are not very local vol-dependent, just as most other exotics.For Asian options you could use Curran's approximation. This is a nice closed form approximation. In the collector's book you can find the formula, it is possible to extent it to cope with term structure for interest rates and vols. I can't imagine you need anything more sophisticated than that for risk management.Good luck.

Hello ElJorrothank you for the advice. The vanilla volatility surfaces are indeed almost flat in the maturity dimension. But the smile is at over 2% for far OTM options and it's probably going to make a difference if I use vanilla or calculated vols for eg. barrier options, though of course the latter may - as you say - be even less appropriate. For which exotic options would you advise me to build the local volatility surface? Can I hope that the surfaces will stay flat?Best regards - Dunbar

Remember that the "local vol model" is just a particular model, presuming something about how the vanilla vol surface is going to move around as the underlying price moves.It might very well be a bad model for describing the market you're dealing with.In G7 fx, for example, local vols are particularly bad - if you try to dynamically hedge a derivative with fx spot using the Deltas it gives you (different than the Black-Scholes Deltas, of course), you often end up with a *worse* hedge in practise than if you'd just used Black-Scholes! The hedging errors come from the fact that the way the vol surface moves around in practise is quite different from what a local vol model predicts.The local vol model has the advantage that it's easy to calibrate and price exotics in a well-defined way, but it often has the decided disadvantage that it's not practically much good.But resa's point is well-made: to price an exotic you can't just grab one of the vanilla implied vols and jam it into the Black-Scholes formula for the exotic. Instead, you need to choose a model, calibrate its parameters to the implied vols, and then use the model with those parameters to price your exotic. Not easy, not even particularly well-defined (because many qualitatively different models can all match the same current implied vols), but that's life.

Hello. Thank you all.Let me sum up:MM reza and mghiggins advise to set up a single model capable of pricing both vanilla and exotic options and calibrate it to quoted vanilla prices. MM mghiggins and ElJorro point out that the task may not be easy and even yield counterproductive results. M ElJorro suggests using directly plain volatilities, this has not been supported by others though.It seems the way I proceed now - based on your kind advice - should depend on the purpose of my calculations. It is neither trading nor hedging options but I need to show some sophistication in my valuation and risk analysis. Would you agree that I should go for local volatility model by building a Derman-Kani implied tree?Best regards - Dunbar

So you're asking what model you should use to look good, and you don't care if it's a good model? It makes a real difference which model you choose - different models can match all the same vanilla prices but yield quite different prices for things like knockouts.That said, an implied tree is easy to put together and relatively fast to calculate (though be careful about how you handle barriers! Convergence can be very slow if you're not). You can price lots of different exotics in a consistent (if incorrect) way. So maybe that's best for your curious application.

hi guys...don't mean to hijack this thread, but can you guys give advice on how to mark-to-market OTC options without any implied vol from exchange traded options to speak of ? what is the common practice ? say we have a convertible bond and we strip out the option component to sell to clients. the underlying stock has no exchange traded option. how do we mark-to-market the option component?also, what if there is an exchange traded option market but the contract specs are diff (strike, maturity) - i know it is 'inaccurate' to use exchange traded implied vols but, what is the common practice for this when this scenario occurs?thanks!

>> the underlying stock has no exchange traded option. how do we mark-to-market the option componentyou can use the time series to calibrate your vol processcf. Wilmott, Issue 5

you mean mark-to-market using historical vol? is that good practice?

Dear mghiggins and all my tutorsof course I want to obtain most correct prices and thus make my model look good. The curiosity of my application stems from the fact that I will use the model exclusively for pricing, so I guess I need not worry about the uselessness of local volatility in hedging. Would you advise me to choose a Derman Kani binomial tree, a Derman Kani Chriss trinomial tree or a Jackwerth generalized binomial tree? I've got Collector's code for the first two but Jackwerth promises much improvement in his article. By the way if I recover a volatility surface for an exotic option from the tree calculations and perform a risk analysis on analytical formulas will I not avoid the problem of smile moving in the opposite direction to spot price?Thank you, best regards - Dunbar

Hi,We trade a lot of equity exotics and each underlying (even if the products is super-exotic) is based on an extended (50 to 300% strike vs. 1m up to 10y/15y) vol surface, based on plain vanilla prices.CiaoEgmont

>> you mean mark-to-market using historical vol? is that good practice? no, you need to switch to risk-neutral measure to have the vol risk-premiumyou can also a jump component to have a higher skew ...