Note on simulation pricing of $\pi$-options

TL;DR

This paper adapts a Monte Carlo algorithm to price $$-options, providing bounds that converge to the true price and demonstrating their application in portfolio protection against market volatility.

Contribution

It introduces a Monte Carlo pricing method for $$-options using simulated price trees, with convergence guarantees and practical portfolio risk management applications.

Findings

Bounds converge to true $$-option price with increased tree depth

Method effectively relates to maximum drawdown in real markets

Numerical analysis supports practical applicability

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.