Paper: arXiv 2302.12439

Authors: Ivan Guo, Nicolas Langrené, Jiahao Wu

Abstract

In this paper, we introduce two novel methods to solve the American-style option pricing problem and its dual form at the same time using neural networks. Without applying nested Monte Carlo, the first method uses a series of neural networks to simultaneously compute both the lower and upper bounds of the option price, and the second one accomplishes the same goal with one global network. The avoidance of extra simulations and the use of neural networks significantly reduce the computational complexity and allow us to price Bermudan options with frequent exercise opportunities in high dimensions, as illustrated by the provided numerical experiments. As a by-product, these methods also derive a hedging strategy for the option, which can also be used as a control variate for variance reduction.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated approach to American option pricing by simultaneously solving primal and dual bounds via neural networks without nested Monte Carlo. While numerical experiments demonstrate strong computational efficiency in high dimensions, full code availability and empirical market testing would enhance reproducibility.

Research Flowchart

  flowchart TD
    A[Goal: Efficiently Price High-Dimensional American Options & Find Dual Bounds] --> B[Inputs: Asset Dynamics & Financial Option Contracts]
    B --> C[Core Methodology: Neural Network-Based Dual Optimization]
    
    C --> D1[Approach 1: Sequential Neural Networks]
    C --> D2[Approach 2: Single Global Neural Network]
    
    D1 & D2 --> E[Computational Process: Non-nested Monte Carlo Trajectory Training]
    
    E --> F[Outcomes: Simultaneous Upper/Lower Bounds & Derived Hedging Strategy]