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Optimal positioning in financial derivatives under mixture distributions

Author

Listed:
  • Rania Hentati

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Luc Prigent

    (THEMA - Théorie économique, modélisation et applications - UCP - Université de Cergy Pontoise - Université Paris-Seine - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper, we study and extend the optimal portfolio positioning problem introduced by Brennan and Solanki (1981) and by Leland (1980). For that purpose, we introduce mixtures of probability distributions to model the log returns of financial assets. In this framework, we provide and analyze the general solution for log return with mixture distributions, in particular for the mixture Gaussian case. Our solution is characterized for arbitrary utility functions and for any risk neutral probability. Moreover, we illustrate the solution for a CRRA utility and for the minimal risk-neutral probability. Lastly, we compare our solution with the optimal portfolio within ambiguity. Our results have significant implications to improve the management of structured financial portfolios.

Suggested Citation

  • Rania Hentati & Jean-Luc Prigent, 2016. "Optimal positioning in financial derivatives under mixture distributions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01299840, HAL.
    • Handle: RePEc:hal:cesptp:hal-01299840
    DOI: 10.1016/j.econmod.2015.02.021
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    1. Brennan, M.J. & Solanki, R., 1981. "Optimal Portfolio Insurance," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 16(3), pages 279-300, September.
    2. Damiano Brigo & Fabio Mercurio, 2002. "Lognormal-Mixture Dynamics And Calibration To Market Volatility Smiles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 427-446.
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    5. Anthony Bonifonte & Turgay Ayer & Benjamin Haaland, 2022. "An Analytics Approach to Guide Randomized Controlled Trials in Hypertension Management," Management Science, INFORMS, vol. 68(9), pages 6634-6647, September.
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    7. Hentati-Kaffel, Rania, 2016. "Structured products under generalized kappa ratio," Economic Modelling, Elsevier, vol. 58(C), pages 599-614.

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    More about this item

    Keywords

    financial portfolio;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G02 - Financial Economics - - General - - - Behavioral Finance: Underlying Principles
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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