CosMethod

The Fang-Oosterlee COS method: a European option price as a cosine series in the risk-neutral density of the log-return, reconstructed from a CharacteristicFunction. Spectral convergence — for a smooth density a few hundred terms give machine-precision accuracy, and a whole strike slice costs one pass of the same phi evaluations.

price = e^{-rT} * sum_{k=0}^{N-1}' Re{ phi(k pi / (b-a)) e^{-i k pi a / (b-a)} } * U_k

where [a, b] is the truncation range from the cumulants and U_k are the payoff cosine coefficients. Puts are taken from the call by parity.