Scaling Invariance and Contingent Claim Pricing Ii: Path-Dependent Contingent Claims

Centrum voor Wiskunde en Informatica, MAS Working Paper No. R9919

19 Pages Posted: 17 Nov 1999

See all articles by Jiri Hoogland

Jiri Hoogland

Centrum voor Wiskunde en Informatica (CWI)

Dimitri Neumann

Centrum voor Wiskunde en Informatica (CWI)

Date Written: July 14, 1999

Abstract

This article is the second one in a series on the use of scaling invariance in finance. In the first paper, we introduced a new formalism for the pricing of derivative securities, which focusses 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 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.

JEL Classification: G13

Suggested Citation

Hoogland, Jiri and Neumann, Dimitri, Scaling Invariance and Contingent Claim Pricing Ii: Path-Dependent Contingent Claims (July 14, 1999). Centrum voor Wiskunde en Informatica, MAS Working Paper No. R9919. Available at SSRN: https://ssrn.com/abstract=180889 or http://dx.doi.org/10.2139/ssrn.180889

Jiri Hoogland (Contact Author)

Centrum voor Wiskunde en Informatica (CWI) ( email )

P.O.Box 94079
MAS
NL-1090 GB Amsterdam
Netherlands
+31(20)5924102 (Phone)
+31(20)5924199 (Fax)

Dimitri Neumann

Centrum voor Wiskunde en Informatica (CWI) ( email )

P.O.Box 94079
MAS
NL-1090 GB Amsterdam
Netherlands
+31(20)5924102 (Phone)
+31(20)5924199 (Fax)

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