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How To Use Self-Similarities To Discover Similarities Of Path-Dependent Options

In: Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II)

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  • ALEXANDER LIPTON

    (Deutsche Bank, Germany)

Abstract

It is well-known that self-similarity is a powerful concept which reveals the fundamental laws of physic. This concept has important financial applications as well. It allows one to study the properties of derivatives from a unified prospective and significantly simplifies their mathematical modelling and hedging. In the present paper, I show how the concept of self-similarity can be used in order to find similarities between various types of path-dependent options and price them in the unified framework. Specifically, I consider lookback, passport, Asian, and imperfectly hedged European options. I present some new important valuation formulas and rederive a few known ones by elementary means.

Suggested Citation

  • Alexander Lipton, 2001. "How To Use Self-Similarities To Discover Similarities Of Path-Dependent Options," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 12, pages 317-334, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812810663_0012
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