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 lower and 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.
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.
R
lower and
the lower and the