Journal of Applied Mathematics
Volume 2005 (2005), Issue 2, Pages 117-125
Integral price formulas for lookback options
1Department of Applied Mathematics, Tongji University, Shanghai 200092, China
2Department of Mathematics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
Received 6 August 2004; Revised 5 November 2004
Copyright © 2005 Chenglong Xu and Yue Kuen Kwok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We derive an integral representation of the price formulas for European options whose terminal payoff involves path-dependent lookback variable. The intricacies in the derivation procedures using the partial differential equation techniques stem from the degenerate nature of the pricing models, where the lookback state variables appear only in the auxiliary conditions but not in the governing differential equations. We also derive a parity relation between the price functions of the floating strike and fixed strike lookback options.