Valuing American Fractional Lookback Options

This study presents an analytical framework for the valuation of American fractional floating‐strike lookback options, taking into account both path dependency and the possibility of early exercise. The proposed pricing methodology is based on the Mellin transform technique, through which we derive and solve the associated partial differential equations governing the pricing functions. A key contribution of this work is the explicit characterization of the early‐exercise premium via an integral equation, in contrast to existing methods that typically rely on implicit expressions obtained through inverse transformations. This explicit form provides a more transparent understanding of the structure and behavior of the early‐exercise premium. Numerical experiments are conducted to confirm the accuracy and stability of the proposed approach in approximating the true option values.