I am using a determinsitc local volatility model to price vanilla options (European and American including discrete dividends). So far, I have been pricing with a generalized binomial tree. However, the model generates fat tails and, as a result, I am experiencing numerical problems at the extremes of the tree which sometimes cause large errors. I have tried a simple truncation scheme but it is proving difficult to generalize in a way sufficient to systematically control the errors. I haven't exhausted all the possibilities and still have some work to do with the debugger tracing exactly how the errors come about, but this is becoming very time-consuming. Does anyone know of a reliable method that I can use? Or should I use a different numerical method (Finite Difference? Is it in your book, Cuchulain?).I have thought about using Curran's "willow" tree, but I don't find his paper transparent enough to implement myself. Does anyone have it programmed? Does anyone know how to contact Curran?

We're using Finite Differences. All standard methods work fine for us. That is Explicit, Fully Implicit and Crank Nicolson. Sorry Cuch, have not yet gotten around to implement Exponential Fitting .Problems we're having from time to time is exploding or complex Local Volatility when using Dupire on a smoothed implied vol surface. This naturally leads to instability ... . To counter explosion we just limit local vol at a certain level. Complex local vol results from a violation of no arbitrage in the implied vol surface, right?Peter