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Quantile hedging for basket derivatives

100%
Barski M.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 1
103-127
EN
The problem of quantile hedging for basket derivatives in the Black-Scholes model with correlation is considered. Explicit formulas for the probability maximizing function and the cost reduction function are derived. Applicability of the results to the widely traded derivatives like digital, quantos, outperformance and spread options is shown.
2
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Integral representations of risk functions for basket derivatives

100%
Barski M.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 4
489-514
EN
The risk minimizing problem $E[l((H-X_T^{x,π})⁺)] \overset{π}{→} min$ 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.
3
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Incompleteness of the bond market with Lévy noise under the physical measure

100%
Barski M.
Banach Center Publications
|
2015
|
tom 104
|
nr 1
61-84
EN
The problem of completeness of the forward rate based bond market model driven by a Lévy process under the physical measure is examined. The incompleteness of market in the case when the Lévy measure has a density function is shown. The required elements of the theory of stochastic integration over the compensated jump measure under a martingale measure are presented and the corresponding integral representation of local martingales is proven.
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