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A Note on Simulation Pricing of π -Options

Author

Listed:
  • Zbigniew Palmowski

    (Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, ul. Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
    These authors contributed equally to this work.)

  • Tomasz Serafin

    (Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, ul. Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
    These authors contributed equally to this work.)

Abstract

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π -option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset’s price. As a result, this algorithm produces the lower and the upper bounds that converge to the true price with the increasing depth of the tree. Under specific parametrization, this π -option is related to relative maximum drawdown and can be used in the real market environment to protect a portfolio against volatile and unexpected price drops. We also provide some numerical analysis.

Suggested Citation

  • Zbigniew Palmowski & Tomasz Serafin, 2020. "A Note on Simulation Pricing of π -Options," Risks, MDPI, vol. 8(3), pages 1-19, August.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:90-:d:405414
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    References listed on IDEAS

    as
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