LOCAL SCALE INVARIANCE AND CONTINGENT CLAIM PRICING II: PATH-DEPENDENT CONTINGENT CLAIMS

J. K. Hoogland () and C. D. D. Neumann ()
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J. K. Hoogland: Centrum voor Wiskunde en Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
C. D. D. Neumann: Centrum voor Wiskunde en Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands

International Journal of Theoretical and Applied Finance (IJTAF), 2001, vol. 04, issue 01, 23-43

Abstract: This article is the second one in a series on the use of local scale invariance in finance. In the first [6], we introduced a new formalism for the pricing of derivative securities, which focuses on tradable objects only, and which completely avoids the use of martingale techniques. In this article we show the use of the formalism in the context of path-dependent options. We derive compact and intuitive formulae for the prices of a whole range of well-known options such as arithmetic and geometric average options, barriers, rebates and lookback options. Some of these have not appeared in the literature before. For example, we find rather elegant formulae for double barrier options with exponentially moving barriers, continuous dividends and all possible configurations of the barriers. The strength of the formalism reveals itself in the ease with which these prices can be derived. This allowed us to pinpoint some mistakes regarding geometric mean options, which frequently appear in the literature. Furthermore, symmetries such as put-call transformations appear in a natural way within the framework.

Keywords: Contingent claim pricing; scale invariance; homogeneity; partial differential equation (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1142/S0219024901000869

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