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Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

Part of: Mathematical finance Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Peter Tankov
Peter Tankov*
Affiliation:
École Polytechnique
*
∗Postal address: Centre de Mathématiques Appliquées, École Polytechnique, 91128 Palaiseau, France. Email address: peter.tankov@polytechnique.org
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Abstract

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Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1]2, or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.

Keywords

CopulaFréchet-Hoeffding boundconcordance orderbasket option

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 91G20: Derivative securities
Type
Research Article
Information
Journal of Applied Probability , Volume 48 , Issue 2 , June 2011 , pp. 389 - 403
Copyright
Copyright © Applied Probability Trust 2011 

References

[1] Dhaene, J. and Goovaerts, M. (1996). Dependency of risks and stop-loss order. ASTIN Bull. 26, 201–212.Google Scholar
[2] Fredricks, G. A. and Nelsen, R. B. (2002). The Bertino family of copulas. In Distributions with Given Marginals and Statistical Modelling, Kluwer, Dordrecht, pp. 81–92.CrossRefGoogle Scholar
[3] Genest, C., Quesada-Molina, J. J., Rodriguez Lallena, J. A. and Sempi, C. (1999). A characterization of quasi-copulas. J. Multivariate Anal. 69, 193–205.CrossRefGoogle Scholar
[4] Hobson, D., Laurence, P. and Wang, T.-H. (2005). Static-arbitrage optimal subreplicating strategies for basket options. Insurance Math. Econom. 37, 553–572.Google Scholar
[5] Hobson, D., Laurence, P. and Wang, T.-H. (2005). Static-arbitrage upper bounds for the prices of basket options. Quant. Finance 5, 329–342.Google Scholar
[6] Kaas, R., Laeven, R. J. A. and Nelsen, R. B. (2009). Worst VaR scenarios with given marginals and measures of association. Insurance Math. Econom. 44, 146–158.Google Scholar
[7] Kingman, J. F. C. and Taylor, S. J. (1966). Introduction to Measure and Probability. Cambridge University Press.CrossRefGoogle Scholar
[8] Müller, A. and Scarsini, M. (2000). Some remarks on the supermodular order. J. Multivariate Anal. 73, 107–119.CrossRefGoogle Scholar
[9] Nelsen, R. B. (2006). An Introduction to Copulas, 2nd edn. Springer, New York.Google Scholar
[10] Nelsen, R. B., Quesada-Molina, J. J., Rodriguez Lallena, J. A. and Úbeda-Flores, M. (2001). Bounds on bivariate distribution functions with given margins and measures of associations. Commun. Statist. Theory Meth. 30, 1155–1162.Google Scholar
[11] Nelsen, R. B., Quesada-Molina, J. J., Rodriguez Lallena, J. A. and Úbeda-Flores, M. (2004). Best-possible bounds on sets of bivariate distribution functions. J. Multivariate Anal. 90, 348–358.Google Scholar
[12] Rapuch, G. and Roncalli, T. (2001). Some remarks on two-asset options pricing and stochastic dependence of asset prices. Tech. Rep., Groupe de Recherche Operationnelle, Credit Lyonnais.Google Scholar
[13] Tchen, A. H. (1980). Inequalities for distributions with given margins. Ann. Appl. Prob. 8, 814–827.Google Scholar