In this work we proposed a new method to estimate local volatility functions with a
non parametric approach. The method is based on the statistical learning literature and
uses gradient boosting with smooth transition trees as base learners. The smoothness
and robustness of the method generates well behaved local volatility functions, capable
of replicating vanilla option prices and the implied volatility surface. Furthermore, the
method proved to be useful for pricing exotic options. We tested the method for simulated
data, Asian calls, Float strike calls and Barrier knockout options.