Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion

Yuri Imamura () and Katsuya Takagi

Asia-Pacific Financial Markets, 2013, vol. 20, issue 1, 81 pages

Abstract: On a multi-assets Black-Scholes economy, we introduce a class of barrier options, where the knock-out boundary is a cone. In this model we apply a generalized reflection principle in a context of the finite reflection group acting on a Euclidean space to give a valuation formula and the semi-static hedge. The result is a multi-dimensional generalization of the put-call symmetry by Bowie and Carr (Risk (7):45–49, 1994 ), Carr and Chou (Risk 10(9):139–145, 1997 ), etc. The important implication of our result is that with a given volatility matrix structure of the multi-assets, one can design a multi-barrier option and a system of plain options, with the latter the former is statically hedged. Copyright Springer Science+Business Media New York 2013

Keywords: Semi-static hedging; Barrier option; Put-call symmetry; Reflection group (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10690-012-9159-7

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