HOW TO USE SELF-SIMILARITIES TO DISCOVER SIMILARITIES OF PATH-DEPENDENT OPTIONS

Alexander Lipton
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Alexander Lipton: Deutsche Bank, Germany

Chapter 12 in Quantitative Analysis in Financial Markets:Collected Papers of the New York University Mathematical Finance Seminar(Volume II), 2001, pp 317-334 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIt 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.

Date: 2001
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