Pricing Bermudan options using regression trees/random forests

TL;DR

This paper explores using regression trees and random forests to estimate continuation values in Bermudan option pricing, offering a potentially more effective approach in high-dimensional settings.

Contribution

It introduces a novel application of regression trees and random forests for Bermudan option pricing, extending the Longstaff-Schwartz algorithm with these machine learning methods.

Findings

Random forests perform well in high-dimensional problems.

Regression trees provide accurate continuation value estimates.

The approach demonstrates convergence properties similar to traditional methods.

Abstract

The value of an American option is the maximized value of the discounted cash flows from the option. At each time step, one needs to compare the immediate exercise value with the continuation value and decide to exercise as soon as the exercise value is strictly greater than the continuation value. We can formulate this problem as a dynamic programming equation, where the main difficulty comes from the computation of the conditional expectations representing the continuation values at each time step. In (Longstaff and Schwartz, 2001), these conditional expectations were estimated using regressions on a finite-dimensional vector space (typically a polynomial basis). In this paper, we follow the same algorithm; only the conditional expectations are estimated using Regression trees or Random forests. We discuss the convergence of the LS algorithm when the standard least squares regression is replaced with regression trees. Finally, we expose some numerical results with regression trees and random forests. The random forest algorithm gives excellent results in high dimensions.