Minimizing the Risk of a Financial Product Using a Put Option |
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| Authors: | Griselda Deelstra Michèle Vanmaele David Vyncke |
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| Institution: | Griselda Deelstra is in the Department of Mathematics, ECARES and Solvay Business School, Université Libre de Bruxelles. Michèle Vanmaele is in the Department of Applied Mathematics and Computer Science, Ghent University. David Vyncke is in the Department of Applied Mathematics and Computer Science, Ghent University. The authors can be contacted via e‐mail: griselda.deelstra@ulb.ac.be, michele.vanmaele@ugent.be, and david.vyncke@ugent.be, respectively. Griselda Deelstra acknowledges financial support of the BNB contract FC0315D00000. Michèle Vanmaele would like to acknowledge the financial support by the BOF project 011/155/04 of Ghent University. The authors thank two anonymous referees for their valuable suggestions to improve the article. |
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| Abstract: | In this article, we elaborate a method for determining the optimal strike price for a put option, used to hedge a position in a financial product such as a basket of shares and a bond. This strike price is optimal in the sense that it minimizes, for a given budget, a class of risk measures satisfying certain properties. Formulas are derived for one single underlying as well as for a weighted sum of underlyings. For the latter we will consider two cases depending on the dependence structure of the components in this weighted sum. Applications and numerical results are presented. |
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