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Pricing Risky Options Simply

Author

Listed:
  • Erik Aurell

    (Matematiska Institutionen, Stockholm Universitet, S-106 91 Stockholm, Sweden;
    Artificial Economy Project, PDC/KTH, S-100 44 Stockholm, Sweden)

  • Sergei I. Simdyankin

    (Artificial Economy Project, PDC/KTH, S-100 44 Stockholm, Sweden;
    Radiophysics Department, University of Nizhny Novgorod, Nizhny Novgorod 603600, Russia)

Abstract

This paper is a follow-up of (Aurell and Życzkowski, 1996) [2] and (Aurellet al.1996) [1]. We show that the prescription of pricing option by minimizing risk can be solved in a way that is quite similar to the Black–Scholes' approach. For a given discrete-time price process we determine an auxillary process, generally a pseudo-probability taking both negative and positive values, such that the price of the option in our prescription is the expected value upon maturation with respect to the auxillary process. We present a conjecture due to G. Wolczyńska that this auxillary process is in fact a (pseudo)-Markov process which admits a very simple description. Numerical results are presented in favor of the conjecture.

Suggested Citation

  • Erik Aurell & Sergei I. Simdyankin, 1998. "Pricing Risky Options Simply," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-23.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:01:n:s0219024998000023
    DOI: 10.1142/S0219024998000023
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    Citations

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    Cited by:

    1. Fedotov, Sergei & Panayides, Stephanos, 2005. "Stochastic arbitrage return and its implication for option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 207-217.
    2. 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.
    3. 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.
    4. Sergei Fedotov & Sergei Mikhailov, 1998. "Option Pricing Model for Incomplete Market," Papers cond-mat/9807397, arXiv.org, revised Aug 1998.

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