A dynamic look-ahead Monte Carlo algorithm for pricing Bermudan options

TL;DR

This paper introduces an adaptive simulation algorithm using nonparametric regression to efficiently price high-dimensional Bermudan options by solving optimal stopping problems with improved accuracy.

Contribution

It presents a novel recursive, data-driven Monte Carlo method that estimates continuation values for Bermudan options, enhancing computational efficiency and convergence analysis.

Findings

Consistent with proven convergence rates

Effective in high-dimensional basket options

Outperforms traditional methods in accuracy

Abstract

Under the assumption of no-arbitrage, the pricing of American and Bermudan options can be casted into optimal stopping problems. We propose a new adaptive simulation based algorithm for the numerical solution of optimal stopping problems in discrete time. Our approach is to recursively compute the so-called continuation values. They are defined as regression functions of the cash flow, which would occur over a series of subsequent time periods, if the approximated optimal exercise strategy is applied. We use nonparametric least squares regression estimates to approximate the continuation values from a set of sample paths which we simulate from the underlying stochastic process. The parameters of the regression estimates and the regression problems are chosen in a data-dependent manner. We present results concerning the consistency and rate of convergence of the new algorithm. Finally, we illustrate its performance by pricing high-dimensional Bermudan basket options with strangle-spread payoff based on the average of the underlying assets.