, Volume 20, Issue 1, pp 71-81

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

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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.