Non-Nested Monte Carlo Dual Bounds for Multi-Exercisable Options

Abstract

We study the optimal marginal value of discrete-time optimal multiple stopping problems and find that it can be formulated as a single optimal stopping optimization as well. Based on this result propose a marginal-value-based lower bound method to achieve a small bound on the iterative error. We further introduce a non-nested upper bound method. The convergence of both methods is analysed. The implementation details and enhancement techniques are discussed as well. Overall, our methods make a good trade-off between the time-efficiency and the tightness in dual bounds.