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In this paper we propose a semi-analytic approach to pricing American optionsfor some time-dependent jump-diffusions models. The idea of the method is tofurther generalize our approach developed for pricing barrier, [Itkin et al.,2021], and American, [Carr and Itkin, 2021; Itkin and Muravey, 2023], optionsin various time-dependent one factor and even stochastic volatility models. Ourapproach i) allows arbitrary dependencies of the model parameters on time; ii)reduces solution of the pricing problem for American options to a simplerproblem of solving an algebraic nonlinear equation for the exercise boundaryand a linear Fredholm-Volterra equation for the the option price; iii) theoptions Greeks solve a similar Fredholm-Volterra linear equation obtained byjust differentiating Eq. (25) by the required parameter.

Semi-analytic pricing of American options in some time-dependent jump-diffusion models