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Semi-analytical pricing of American options in a time-dependentOrnstein-Uhlenbeck model was presented in [Carr, Itkin, 2020]. It was shownthat to obtain these prices one needs to solve (numerically) a nonlinearVolterra 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 pricesfollow. It was also shown that computationally this method is as efficient asthe forward finite difference solver while providing better accuracy andstability. Later this approach called "the Generalized Integral transform"method has been significantly extended by the authors (also, in cooperationwith Peter Carr and Alex Lipton) to various time-dependent one factor, andstochastic volatility models as applied to pricing barrier options. However,for American options, despite possible, this was not explicitly reportedanywhere. In this paper our goal is to fill this gap and also discuss whichnumerical method (including those in machine learning) could be efficient tosolve the corresponding Volterra integral equations.

American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support