Pricing Discrete Lookback Options via Complex Fourier Series in Regime‐Switching Jump‐Diffusion Models

ABSTRACT This study presents an efficient pricing method for discrete lookback options under a regime‐switching jump‐diffusion model. By employing a complex Fourier series expansion, we derive semi‐closed‐form pricing formulas for both floating‐ and fixed‐strike options. Numerical experiments demonstrate that the proposed approach achieves a speedup of nearly two orders of magnitude over Monte Carlo simulations while maintaining comparable accuracy. In the tested settings, the complex Fourier series and Fourier cosine methods deliver comparable prices and runtimes. Sensitivity analysis further reveals that neglecting regime shifts or jump risks leads to substantial pricing biases. These findings suggest that the complex Fourier series method provides an efficient alternative for valuing discrete lookback options in the benchmark settings considered.