Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion
Yuri Imamura, Katsuya Takagi
TL;DR
This paper introduces a class of barrier options in a multi-asset Black-Scholes model, utilizing a generalized reflection principle to derive valuation formulas and semi-static hedging strategies.
Contribution
It develops a novel application of the generalized reflection principle for multi-dimensional Brownian motion to price and hedge barrier options.
Findings
Derived explicit valuation formulas for the new barrier options.
Established semi-static hedging strategies based on the reflection principle.
Extended the reflection principle to a multi-dimensional setting.
Abstract
On a multi-assets Black-Scholes economy, we introduce a class of barrier options. 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.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models · Complex Systems and Time Series Analysis