Kriging Metamodels and Experimental Design for Bermudan Option Pricing

TL;DR

This paper introduces stochastic kriging models and experimental design strategies to enhance the efficiency of Bermudan option pricing within the Regression Monte Carlo framework, significantly reducing simulation costs.

Contribution

It proposes the use of Gaussian process meta-models and experimental design principles to improve RMC methods for Bermudan option valuation.

Findings

Krige-based models improve approximation quality.

Design of experiments reduces simulation budget.

Adaptive batching enhances signal-to-noise ratio.

Abstract

We investigate two new strategies for the numerical solution of optimal stopping problems within the Regression Monte Carlo (RMC) framework of Longstaff and Schwartz. First, we propose the use of stochastic kriging (Gaussian process) meta-models for fitting the continuation value. Kriging offers a flexible, nonparametric regression approach that quantifies approximation quality. Second, we connect the choice of stochastic grids used in RMC to the Design of Experiments paradigm. We examine space-filling and adaptive experimental designs; we also investigate the use of batching with replicated simulations at design sites to improve the signal-to-noise ratio. Numerical case studies for valuing Bermudan Puts and Max-Calls under a variety of asset dynamics illustrate that our methods offer significant reduction in simulation budgets over existing approaches.