Lookback options and diffusion hitting times: a spectral expansion approach
The author applies the spectral expansion approach to lookback options. Some general results for lookback options are presented when the underlying follows a one-dimensional diffusion and lookback prices are expressed in terms of hitting time distributions. A spectral decomposition of the first hitting time distribution of a one-dimensional diffusion is given. Then the diffusion with constant elasticity of variance is considered and analytical solutions for lookback options are obtained in terms of spectral expansions. This spectral expansion can serve as benchmarks for numerical methods. The specific advantages of spectral expansions are demonstrated.
scientific article; zbMATH DE number 2169540