Do exchanges and institutions use Black-Scholes or implied volatility trees or other forms of binomial trees to price options? Just curious.
Can't speak for all institutions - but here they use Black-Scholes for European options and binomial trees for American. However these are just the defaults - systems here allow the managers to price using a variety of methods.
I know that institutions do use Black-Scholes and binomial models. They claim that they have the "proprietary" models, but their quotes usually are suspiciously close to the values suggested by the models. ThetaSpec
There's no reason for the "proprietary" models to give significantly different values as binomial and B-S are not that bad, if you know what I mean.
No-one in their right mind uses the bog-standard Black-Scholes-Merton model. It makes far too many simplifying assumptions. Its a start, and that is all. Fisher Black himself wrote a paper "How to Use the Holes in Black-Scholes" about this a while back.
Duh, the values better be spot on market, otherwise the desk has a big problem. What is different in "proprietary" models is the treatment of the greeks, which is far more important.
Does not really matter and the distinction between exotics and vanilla is pretty blurry. Are you asking a philosophical question or you're asking how the exotics market works? On a "holistic" level, any desk that is very far off market should and will realize that something is wrong and will revise it's market assumptions and model parameters to be on market. The example is cliquets in the equity world and CMS spread options in the rates world, that people price with a vast variety of models but the prices trade very tightly. That's because everyone tweaks the various model parameters to match the market prices. When in competition on less liquid stuff, you see people quote all over the place, i have seen the markets that was 2-3 points wide on an 11 point option. However, most of it has nothing to do with the model and more with the market assumptions. For instance, on basket options, your forward and correlation assumptions will be far more significant then using basket approximation as opposed to some smart MC-basket model.
Thanks for your insight. It was more of a philosophical question. I also wonder how much of a liquidity premium one should price in, when checking exotic derivatives quotes from the counterparties? In the example above you mentioned 20-30%? It has to be an exception rather than the rule. What do you do, if you don't mind me asking?