A general method for debiasing a Monte Carlo estimator

TL;DR

This paper introduces a general unbiased estimation method for processes derived from numerical schemes or Monte Carlo methods, applicable to various problems like integration, root-finding, and option pricing, improving accuracy over biased estimators.

Contribution

The paper presents a novel, general scheme for unbiased estimation of limiting process values, with error estimates, applicable across multiple numerical and stochastic methods.

Findings

Unbiased estimators achieved for numerical integrals, root-finding, and option pricing.

Standard error estimates provided alongside unbiased estimators.

Method demonstrated on Heston Stochastic Volatility model.

Abstract

Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation. We will assume that we can sample from the distribution of the process from time 0 to finite time n. We propose a scheme for unbiased estimation of the limiting value of the process, together with estimates of standard error and apply this to examples including numerical integrals, root-finding and option pricing in a Heston Stochastic Volatility model. This results in unbiased estimators in place of biased ones i nmany potential applications.