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A General Methodology To Price And Hedge Derivatives In Incomplete Markets

Author

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  • ERIK AURELL

    (Matematiska Institutionen, Stockholms Universitet, S-106 91 Stockholm, Sweden)

  • ROBERTO BAVIERA

    (Dipartimento di Fisica, Università dell'Aquila and Istituto Nazionale Fisica della Materia, Via Vetoio, I-67010 Coppito, L'Aquila, Italy)

  • OLA HAMMARLID

    (Institutionen för Matematisk Statistik och Försäkringsmatematik, Stockholms Universitet, S-106 91 Stockholm, Sweden)

  • MAURIZIO SERVA

    (Dipartimento di Matematica, Università dell'Aquila and Istituto Nazionale Fisica della Materia, Via Vetoio, I-67010 Coppito, L'Aquila, Italy)

  • ANGELO VULPIANI

    (Dipartimento di Fisica, Università di Roma "La Sapienza" and Istituto Nazionale Fisica della Materia, P.le A. Moro 2, I-00185 Roma, Italy)

Abstract

We introduce and discuss a general criterion for the derivative pricing in the general situation of incomplete markets, we refer to it as the No Almost Sure Arbitrage Principle. This approach is based on the theory of optimal strategy in repeated multiplicative games originally introduced by Kelly. As particular cases we obtain the Cox–Ross–Rubinstein and Black–Scholes in the complete markets case and the Schweizer and Bouchaud–Sornette as a quadratic approximation of our prescription. Technical and numerical aspects for the practical option pricing, as large deviation theory approximation and Monte Carlo computation are discussed in detail.

Suggested Citation

  • Erik Aurell & Roberto Baviera & Ola Hammarlid & Maurizio Serva & Angelo Vulpiani, 2000. "A General Methodology To Price And Hedge Derivatives In Incomplete Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-24.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:01:n:s0219024900000024
    DOI: 10.1142/S0219024900000024
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    Cited by:

    1. Jing Peng & Pengyu Wei & Zuo Quan Xu, 2022. "Relative growth rate optimization under behavioral criterion," Papers 2211.05402, arXiv.org.
    2. Pengyu Wei & Zuo Quan Xu, 2021. "Dynamic growth-optimum portfolio choice under risk control," Papers 2112.14451, arXiv.org.
    3. Michael A. H. Dempster & Igor V. Evstigneev & Klaus R. Schenk-hoppe, 2007. "Volatility-induced financial growth," Quantitative Finance, Taylor & Francis Journals, vol. 7(2), pages 151-160.
    4. Aurell, Erik & Baviera, Roberto & Hammarlid, Ola & Serva, Maurizio & Vulpiani, Angelo, 2000. "Growth optimal investment and pricing of derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 505-521.

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