Scale invariance and contingent claim pricing

Jiri Hoogland and Dimitri Neumann ()
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Jiri Hoogland: CWI, Amsterdam

Finance from University Library of Munich, Germany

Abstract: Prices of tradables can only be expressed relative to each other at any instant of time. This fundamental fact should therefore also hold for contingent claims, i.e. tradable instruments, whose prices depend on the prices of other tradables. We show that this property induces a local scaling invariance in the problem of pricing contingent claims. Due to this symmetry we do {\it not\/} require any martingale techniques to arrive at the price of a claim. If the tradables are driven by Brownian motion, we find, in a natural way, that this price satisfies a PDE. Both possess a manifest gauge-invariance. A unique solution can only be given when we impose restrictions on the drifts and volatilities of the tradables, i.e. the underlying market structure. We give some examples of the application of this PDE to the pricing of claims. In the Black- Scholes world we show the equivalence of our formulation with the standard approach. It is stressed that the formulation in terms of tradables leads to a significant conceptual simplification of the pricing-problem.

Keywords: contingent claim pricing; scale-invariance; homogeneity; partial differential equation (search for similar items in EconPapers)
JEL-codes: G12 (search for similar items in EconPapers)
Pages: 17 pages
Date: 1999-07-16
Note: Type of Document - PDF; prepared on NT/Latex; to print on PDF printer; pages: 17 . See also http://www.cwi.nl/~jiri for postscript version version
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Citations: View citations in EconPapers (7)

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