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Note on simulation pricing of $\pi$-options

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  • Zbigniew Palmowski
  • Tomasz Serafin

Abstract

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman (1997) to price a $\pi$-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 $\pi$-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. "Note on simulation pricing of $\pi$-options," Papers 2007.02076, arXiv.org, revised Aug 2020.
    • Handle: RePEc:arx:papers:2007.02076
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    References listed on IDEAS

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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
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