Practical policy iteration: Generic methods for obtaining rapid and tight bounds for Bermudan exotic derivatives using Monte Carlo simulation

摘要

We introduce a set of improvements which allow the calculation of very tight lower bounds for Bermudan derivatives using Monte Carlo simulation. These tight lower bounds can be computed quickly, and with minimal hand-crafting. Our focus is on accelerating policy iteration to the point where it can be used in similar computation times to the basic least-squares approach, but in doing so introduce a number of improvements which can be applied to both the least-squares approach and the calculation of upper bounds using the Andersen-Broadie method. The enhancements to the least-squares method improve both accuracy and efficiency. Results are provided for the displaced-diffusion LIBOR market model, demonstrating that our practical policy iteration algorithm can be used to obtain tight lower bounds for cancellable CMS steepener, snowball and vanilla swaps in similar times to the basic least-squares method.