Pricing American option with a slow-varying stochastic factor

In this paper, we investigate the pricing of American options under a slowly varying stochastic volatility framework, which effectively captures the long-term dynamics of the underlying asset. Employing an asymptotic expansion method, we derive a new analytical approximation for both the option price and the associated optimal exercise boundary. To further enhance computational efficiency, we adopt Kim’s integral equation approach for the leading-order term. In addition, we provide a rigorous error analysis that establishes explicit accuracy guarantees, thereby filling an important gap in the existing literature.