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On Minimizing Risk in Incomplete Markets Option Pricing Models

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  • Ola Hammarlid

    (Department of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden)

Abstract

I study the Bouchaud–Sornette, Schweizer and Schäl way of pricing options, presenting the methodology in accordance with Bouchaud–Sornette. The definitions of the wealth balance and risk from trading in options and stocks are presented. The problem of finding a risk minimizing strategy in an incomplete market model where a perfect hedge is not possible is analyzed. Using this strategy according to the approach of Bouchaud and Sornette the option is priced by a fair game condition. In this article I establish the equivalence between global and local risk minimization and prove an option price conjecture of Wolczyńska. I also investigate optimality for a stock portfolio with extra profit.

Suggested Citation

  • Ola Hammarlid, 1998. "On Minimizing Risk in Incomplete Markets Option Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 227-233.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:02:n:s0219024998000126
    DOI: 10.1142/S0219024998000126
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    Citations

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    Cited by:

    1. Sergei Fedotov & Sergei Mikhailov, 1998. "Option Pricing Model for Incomplete Market," Papers cond-mat/9807397, arXiv.org, revised Aug 1998.
    2. N. Josephy & L. Kimball & A. Nagaev & M. Pasniewski & V. Steblovskaya, 2006. "An Algorithmic Approach to Non-self-financing Hedging in a Discrete-Time Incomplete Market," Papers math/0606471, arXiv.org.
    3. 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.
    4. E. Aurell & R. Baviera & O. Hammarlid & M. Serva & A. Vulpiani, 1998. "A general methodology to price and hedge derivatives in incomplete markets," Papers cond-mat/9810257, arXiv.org, revised Apr 1999.
    5. Erik Aurell & Roberto Baviera & Ola Hammarlid & Maurizio Serva & Angelo Vulpiani, 1999. "Growth Optimal Investment and Pricing of Derivatives," Papers cond-mat/9910212, arXiv.org.
    6. Pinn, Klaus, 2000. "Minimal variance hedging of options with student-t underlying," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 276(3), pages 581-595.
    7. Sergei Fedotov & Sergei Mikhailov, 2001. "Option Pricing For Incomplete Markets Via Stochastic Optimization: Transaction Costs, Adaptive Control And Forecast," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 179-195.

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