Unbiased simulation of Asian options

ArXiv ID: 2504.16349 “View on arXiv”

Authors: Bruno Bouchard, Xiaolu Tan

Abstract

We provide an extension of the unbiased simulation method for SDEs developed in Henry-Labordere et al. [“Ann Appl Probab. 27:6 (2017) 1-37”] to a class of path-dependent dynamics, pertaining for Asian options. In our setting, both the payoff and the SDE’s coefficients depend on the (weighted) average of the process or, more precisely, on the integral of the solution to the SDE against a continuous function with bounded variations. In particular, this applies to the numerical resolution of the class of path-dependent PDEs whose regularity, in the sens of Dupire, is studied in Bouchard and Tan [“Ann. I.H.P., to appear”].

Keywords: Unbiased Simulation, Stochastic Differential Equations (SDEs), Asian Options, Path-Dependent Dynamics, Dupire Regularity, Options

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper is highly mathematical, featuring a complex extension of the unbiased simulation method to path-dependent SDEs, requiring deep PDE and Malliavin calculus, leading to a high math score. The empirical rigor is low as the excerpt focuses on theoretical derivations and provides only a brief mention of numerical examples without any code, backtests, or implementation details.
  flowchart TD
    A["Research Goal<br>Extend unbiased simulation for SDEs<br>to path-dependent Asian option dynamics"] --> B["Input: Asian Option Model<br>Payoff & SDE coefficients<br>depend on weighted process average"]
    B --> C["Key Methodology<br>Extension of Henry-Labordere et al.<br>method to path-dependent setting<br>using integral representation"]
    C --> D["Computational Process<br>Unbiased Monte Carlo simulation<br>of SDE solutions against continuous<br>function with bounded variations"]
    D --> E["Outcomes<br>1. Unbiased estimator for Asian options<br>2. Numerical resolution of path-dependent PDEs<br>3. Analysis of Dupire regularity<br>in Bouchard & Tan framework"]