Integral representations of risk functions for basket derivatives
Volume 39 / 2012
Applicationes Mathematicae 39 (2012), 489-514
MSC: Primary 91B30, 91B24; Secondary 91B70.
DOI: 10.4064/am39-4-6
Abstract
The risk minimizing problem $\mathbf{E}[l((H-X_T^{x,\pi})^{+})]\overset{\pi}{\rightarrow}\min$ 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.
