The Fourier cosine series expansion method for pricing European options. Derives the COS formula from the characteristic function of the log-price process, covers chi and psi payoff coefficients, truncation range selection, and demonstrates convergence under geometric Brownian motion.

Monte Carlo simulation for pricing European, digital and Asian options under Black-Scholes dynamics. Covers convergence properties, antithetic variates, bump-and-revalue sensitivity estimation, and control variates for variance reduction.