Can anyone point me to some papers on calibrating local volatility models to American exercise options?

Ditto, although I'm not so concerned about the fitting but the implications of using American over Europeans.Although, I had thought about producing an implied volatility surface and producing a local vol surface from this. The implied surface could be 'guess & check' fitted (the way a trader might tweak the surface on the fly) to market prices giving the constant vol that would give the market price wrt whatever model you are using. Alternatively you could fit using any numerical fitting procedure depending on the form of your vol surface.From this implied surface the local surface can be derived (although I'd like some paper showing this to confirm my own calculations). Some question I am yet to answer (so please, feel free):1. Would this the surface I describe "allow the calculation of the fair values and exposures of all (standard and exotic) option, consistent with all the initial liquid option prices"? (Dermal et al 1995 - they use European options to calibrate, not American).2. Local vol surface (ie deterministic but level/time dependant volatility) vs stochastic vol in terms of efficiency, tractability and accuracy.3. Why Paul consider local vol surfaces 'evil'. That has an ominous sound to it.

In the following paper,L. Andersen and R. Brotherton Ratcliffe, “The equity option volatility smile: an implicitfinite- difference approach”. Journal of Computation Finance, Volume 1, Number 2 (1997).You have a finite difference method to solve European option.It is just like a Binomial tree, and I think it will be easy to introduce the early exercise feature.The implied binomial tree approac is also a solution.

Concerning the original question, does this even make sense to calibrate local volatility model to American options? I mean the American option is about forward probability distributions, while the local volatility model (as it is from 1994) is only about unconditional probability distributions.I am just impressed by the article of Elie Ayache (2007) Dial 33 for your local cleaner where he criticizes the local volatility model.However, I agree that it makes sense to calibrate local Lévy models to American option prices.Peter

QuoteOriginally posted by: dobranszkyConcerning the original question, does this even make sense to calibrate local volatility model to American options? I mean the American option is about forward probability distributions, while the local volatility model (as it is from 1994) is only about unconditional probability distributions.I am just impressed by the article of Elie Ayache (2007) Dial 33 for your local cleaner where he criticizes the local volatility model.Both your argument and Ayache's paper employ a very naive and limited concept of local volatility. It seems to me that Ayache, in particular, has set up a straw man, because his idea of local volatility is limited to Dupire's non-parametric model which he then contrasts with stochastic volatility models.I prefer to think of local volatility as a deterministic function of local variables that may be themselves stochastic and are not limited to time and price. Someone told me here some time ago in another thread that dependence of the volatility on stochastic variables is really a stochastic volatility model, not a local volatility model. But I think that is a very misleading idea since even Dupire's model is a stochastic volatility by that criterion (it depends on the stochastic price). To me, the essence of the term "stochastic volatility" is that it centers around specifically stochastic concepts like "volatility of volatility", not merely that it depends on stochastic variables. A local volatility model, on the other hand, is a deterministic function that can be used to calculate the local volatility in a pricing tree or finite difference grid, by projecting not just the volatility function itself, but also the local values of the dependent variables (other than that for which one builds the tree/grid) into the future, whether they are strictly stochastic or not, by substituting their statistical behavior with representative deterministic functions (e.g. some sort of conditional expectation function of time). The end result is that, for given current conditions, derivative pricing can be done with what is a strictly deterministic volatility function of time and the tree variable (e.g. price). The essential difference with Dupire lies not with the stochasticity, but that there is a parametrization that is intended to reflect detectable dynamics and current conditions.Perhaps what I have described could be better known as instantaneous volatility, but even that fails to make the distinction between local determinism and pure stochasticity. The usual distinction between local volatility and stochastic volatility as made by Ayache, is an artificial set-up to my mind. The problems with Dupire's non-parametric model (it's instability, and incompatibility with implied volatility dynamics) has been known for many years and is relevant even to vanilla options. It doesn't even describe the underlying asset price series!! One doesn't need to to bring in exotics to point out its failings. To keep re-hashing these problems and fail to distinguish Dupire's model from locally deterministic models in general seems to me to be a pointless exercise.