  A popular approach to nonparametric option pricing is the Minimum Cross
Entropy (MCE) method based on minimization of the relative Kullback-Leibler
entropy of the price density distribution and a given reference density, with
observable option prices serving as constraints. When market prices are noisy,
the MCE method tends to overfit the data and often becomes unstable. We propose
a non-parametric option pricing method whose input are noisy market prices of
arbitrary number of European options with arbitrary maturities. Implied
transition densities are calculated using the Bayesian inverse theory with
entropic priors, with a reference density which may be estimated by the
algorithm itself. In the limit of zero noise, our approach is shown to reduce
to the canonical MCE method generalized to a multi-period case. The method can
be used for a non-parametric pricing of American/Bermudan options with a
possible weak path dependence.
