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Multiasset Derivatives and Joint Distributions of Asset Prices

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Inspired by Finance

Abstract

Several of multiasset derivatives like basket options or options on the weighted maximum of assets exhibit the property that their prices determine uniquely the underlying asset distribution. Related to that the question how to retrieve this distributions from the corresponding derivatives quotes will be discussed. On the contrary, the prices of exchange options do not uniquely determine the underlying distributions of asset prices and the extent of this non-uniqueness can be characterised. The discussion is related to a geometric interpretation of multiasset derivatives as support functions of convex sets. Following this, various symmetry properties for basket, maximum and exchange options are discussed alongside with their geometric interpretations and some decomposition results for more general payoff functions.

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Notes

  1. 1.

    For markets with transaction costs we refer to [32] and the literature cited therein.

  2. 2.

    In relation to this it is stressed e.g. in [20] that a general analysis of financial markets should also consider situations where prices, at least for some instruments, can be negative.

  3. 3.

    Note that here we deal with max-zonoids and not the ℓ p -zonoids from Example 4.

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Acknowledgements

The authors are grateful to Thorsten Rheinländer for inspiring discussions. This work was supported by the Swiss National Science Foundation Grant Nr. 200021-126503.

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Authors and Affiliations

  1. Department of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5, 3012, Bern, Switzerland

    Ilya Molchanov & Michael Schmutz

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  1. Ilya Molchanov
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Correspondence to Ilya Molchanov .

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Editors and Affiliations

  1. Labo. Mathématiques U.F.R. des Sciences et Technologie, Université de Franche-Comté, Besancon, France

    Yuri Kabanov

  2. School of Mathematics & Statistics, University of Sydney, Sydney, New South Wales, Australia

    Marek Rutkowski

  3. Depts. of Mathematics and IROM, McCombs School of Business, The University of Texas at Austin, Austin, Texas, USA

    Thaleia Zariphopoulou

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Molchanov, I., Schmutz, M. (2014). Multiasset Derivatives and Joint Distributions of Asset Prices. In: Kabanov, Y., Rutkowski, M., Zariphopoulou, T. (eds) Inspired by Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-02069-3_20

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