Lookback options and diffusion hitting times: A spectral expansion approach

Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the options lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an analytical characterization of lookback option prices in terms of spectral expansions. In particular, analytical solutions for lookback options under the constant elasticity of variance (CEV) diffusion are obtained.Received: 1 October 2003, Mathematics Subject Classification: 60J35, 60J60, 60G70JEL Classification: G13The author thanks Phelim Boyle for bringing the problem of pricing lookback options under the CEV process to his attention and for useful discussions and Viatcheslav Gorovoi for computational assistance. This research was supported by the U.S. National Science Foundation under grants DMI-0200429 and DMS-0223354.