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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," Post-Print hal-01299840, HAL.
    • Handle: RePEc:hal:journl:hal-01299840
    DOI: 10.1016/j.econmod.2015.02.021
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    References listed on IDEAS

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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. Hentati Rania & Prigent Jean-Luc, 2011. "On the maximization of financial performance measures within mixture models," Statistics & Risk Modeling, De Gruyter, vol. 28(1), pages 63-80, March.
    3. Ameur, H. Ben & Prigent, J.L., 2013. "Optimal portfolio positioning under ambiguity," Economic Modelling, Elsevier, vol. 34(C), pages 89-97.
    4. 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.
    5. J. L. Lesne & J. L. Prigent, 2001. "A General Subordinated Stochastic Process For Derivatives Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 121-146.
    6. Melick, William R. & Thomas, Charles P., 1997. "Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 32(1), pages 91-115, March.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Leland, Hayne E, 1980. "Who Should Buy Portfolio Insurance?," Journal of Finance, American Finance Association, vol. 35(2), pages 581-594, May.
    9. Prigent, J.L., 1997. "Incomplete Markets: Convergence of Options Values under the Minimal Martingale Measure. The Multidimensional Case," Papers 9735, Paris X - Nanterre, U.F.R. de Sc. Ec. Gest. Maths Infor..
    10. K. E. Basford & G. J. McLachlan, 1985. "Likelihood Estimation with Normal Mixture Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 282-289, November.
    11. Alexander, Carol, 2004. "Normal mixture diffusion with uncertain volatility: Modelling short- and long-term smile effects," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2957-2980, December.
    12. P. Carr & D. Madan, 2001. "Optimal positioning in derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 19-37.
    13. Robert J. Ritchey, 1990. "Call Option Valuation For Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, December.
    14. Bertrand, P. & lesne, J.-P. & Prigent, J.-L., 2000. "Gestion de portefeuille avec garantie: l'allocation optimale en actifs derives," G.R.E.Q.A.M. 00a03, Universite Aix-Marseille III.
    15. Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
    16. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, Winter.
    17. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    18. Jean-Luc Prigent, 1999. "Incomplete markets: convergence of options values under the minimal martingale measure," Post-Print hal-03679524, HAL.
    19. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    20. N/A, 1996. "Note:," Foreign Trade Review, , vol. 31(1-2), pages 1-1, January.
    21. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    22. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    4. Hentati-Kaffel, Rania, 2016. "Structured products under generalized kappa ratio," Economic Modelling, Elsevier, vol. 58(C), pages 599-614.
    5. repec:ipg:wpaper:2014-468 is not listed on IDEAS
    6. repec:ipg:wpaper:2014-531 is not listed on IDEAS
    7. repec:ipg:wpaper:2014-510 is not listed on IDEAS

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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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