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Some Lookback Option Pricing Problems

In: Recent Developments In Mathematical Finance

Author

Listed:
  • Xin Guo

    (IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA)

Abstract

We review some path-dependent option pricing problems in the financial market (Black-Scholes or incomplete) in the context of optimal stopping problems. Our focus is on the effectiveness and the limitations of the well-known technique of the "principle of smooth fit". We demonstrate concrete examples where this principle is sufficient in deriving closed-form solutions. We also provide cases where the smooth fit is necessary but not sufficient. We finally discuss an optimal stopping problem with regime switching where we extend the technique of smooth fit to allow instantaneous and discontinuous jumps to obtain closed-form solutions for pricing exotic options.

Suggested Citation

  • Xin Guo, 2001. "Some Lookback Option Pricing Problems," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 4, pages 39-48, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0004
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