Integral representations of risk functions for basket derivatives

Micha{\l} Barski

Papers from arXiv.org

Abstract: The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\longrightarrow}\min$ in the multidimensional Black-Scholes framework is studied. Specific formulas for the minimal risk function and the cost reduction function for basket derivatives are shown. Explicit integral representations for the risk functions for $l(x)=x$ and $l(x)=x^p$, with $p>1$ for digital, quantos, outperformance and spread options are derived.

Date: 2011-02, Revised 2016-01
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Published in Applicationes Mathematicae, 2012, 39, 489-514

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