Solving the Black-Scholes PDE on a grid. The explicit FTCS scheme and the implicit Crank-Nicolson scheme for a European call, the two spatial grids (S and log S) and the coefficients each requires, conditional stability, boundary conditions, and convergence to the analytical value.

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.