Chapter 8 Discrete Barrier and Lookback Options

Discrete barrier and lookback options are among the most popular path-dependent options in markets. However, due to the discrete monitoring policy almost no ana-lytical solutions are available for them. We shall focus on the following methods for discrete barrier and lookback option prices: (1) Broadie–Yamamoto method based on fast Gaussian transforms. (2) Feng–Linetsky method based on Hilbert transforms. (3) A continuity correction approximation. (4) Howison–Steinberg approximation based on the perturbation method. (5) A Laplace inversion method based on Spitzer’s iden-tity. This survey also contains a new (more direct) derivation of a constant related to the continuity correction approximation.