Note on simulation pricing of $π$-options

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman (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.

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