Refinements and Numerical Error Studies of the COS Method for Barrier and Bermudan Options under Heston Dynamics

This thesis investigates the application of the Fourier–cosine method to European-style discretely monitored barrier options and Bermudan options under the Heston Stochastic Volatility model, with emphasis on Feller-violating regimes where numerical challenges are most pronounced. A Refined–COS implementation is proposed, featuring safeguarded computation of the log–variance truncation interval and a robust procedure for determining the Bermudan optimal exercise boundary. Benchmark comparisons with high-accuracy Almost-Exact Scheme Monte Carlo simulations reveal clear convergence patterns: single-barrier options converge rapidly, while long-maturity contracts and double-barrier options remain more demanding, and boundary-location errors dominate the Bermudan option pricing bias for in-the-money contracts. Oscillatory artefacts in the COS density reconstruction are studied, and several spectral filters are tested in barrier option pricing; however, their impact on accuracy is limited and not sufficiently systematic to constitute a reliable improvement. The results provide a transparent and reproducible framework for option valuation under Heston dynamics and highlight key sensitivities that arise when the Feller condition is violated.