Pricing American Options using Machine Learning Algorithms

Paper: arXiv 2409.03204

Abstract

This study investigates the application of machine learning algorithms, particularly in the context of pricing American options using Monte Carlo simulations. Traditional models, such as the Black-Scholes-Merton framework, often fail to adequately address the complexities of American options, which include the ability for early exercise and non-linear payoff structures. By leveraging Monte Carlo methods in conjunction Least Square Method machine learning was used. This research aims to improve the accuracy and efficiency of option pricing. The study evaluates several machine learning models, including neural networks and decision trees, highlighting their potential to outperform traditional approaches. The results from applying machine learning algorithm in LSM indicate that integrating machine learning with Monte Carlo simulations can enhance pricing accuracy and provide more robust predictions, offering significant insights into quantitative finance by merging classical financial theories with modern computational techniques. The dataset was split into features and the target variable representing bid prices, with an 80-20 train-validation split. LSTM and GRU models were constructed using TensorFlow’s Keras API, each with four hidden layers of 200 neurons and an output layer for bid price prediction, optimized with the Adam optimizer and MSE loss function. The GRU model outperformed the LSTM model across all evaluated metrics, demonstrating lower mean absolute error, mean squared error, and root mean squared error, along with greater stability and efficiency in training.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper incorporates advanced mathematical concepts like stochastic differential equations and risk-neutral pricing but also details specific ML implementations, hyperparameters, and empirical metrics (MAE, MSE, RMSE) with a clear dataset split, indicating a balance of theoretical and practical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Pricing American Options<br>using ML"] --> B["Data Preparation<br>80-20 Train-Test Split<br>Features & Bid Price Target"]

  B --> C{"Machine Learning Models"}
  C --> D["LSTM Model<br>4 Layers, 200 Neurons"]
  C --> E["GRU Model<br>4 Layers, 200 Neurons"]

  D & E --> F["Computational Process<br>Monte Carlo Simulation +<br>Least Square Method<br>Optimized with Adam/MSE"]

  F --> G["Key Findings & Outcomes"]
  G --> H["GRU Outperforms LSTM<br>Lower MAE, MSE, RMSE"]
  G --> I["ML Enhanced Pricing<br>Accuracy & Robustness"]
  G --> J["Efficient Integration<br>Classical Finance +<br>Modern Computation"]

Cited References (41)

1. The pricing of options and corporate liabilities (1973)
2. Deep Learning in Option Pricing (2023)
3. American option pricing with machine learning: An extension of the Longstaff-Schwartz method (2021)
4. Applications of option-pricing theory: twenty-five years later (1998)
5. Parametric models and non-parametric machine learning models for predicting option prices: Empirical comparison study over KOSPI 200 Index options (2014)
6. Recurrent neural networks (rnns): A gentle introduction and overview (2019) — link
7. Convergence of the least squares Monte Carlo approach to American option valuation (2004)
8. Brownian motion with a several-dimensional time (1963)

0 of 41 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.