Monte Carlo Bounds for Game Options Including Convertible Bonds

Abstract

We introduce two new methods to calculate bounds for zero-sum game options using Monte Carlo simulation. These extend and generalise the duality results of Haugh-Kogan/Rogers and Jamshidian to the case where both parties of a contract have Bermudan optionality. It is shown that the Andersen-Broadie method can still be used as a generic way to obtain bounds in the extended framework, and we apply the new results to the pricing of convertible bonds by simulation.

Keywords: game option, convertible bond, Monte Carlo, bounds, duality, Rogers, Jamshidian, Andersen-Broadie

JEL Classification: C, C6, C63, C7, C72, C73, G13