  Semi-analytical pricing of American options in a time-dependent
Ornstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shown
that to obtain these prices one needs to solve (numerically) a nonlinear
Volterra integral equation of the second kind to find the exercise boundary
(which is a function of the time only). Once this is done, the option prices
follow. It was also shown that computationally this method is as efficient as
the forward finite difference solver while providing better accuracy and
stability. Later this approach called "the Generalized Integral transform"
method has been significantly extended by the authors (also, in cooperation
with Peter Carr and Alex Lipton) to various time-dependent one factor, and
stochastic volatility models as applied to pricing barrier options. However,
for American options, despite possible, this was not explicitly reported
anywhere. In this paper our goal is to fill this gap and also discuss which
numerical method (including those in machine learning) could be efficient to
solve the corresponding Volterra integral equations.
