Leveraging Machine Learning for High-Dimensional Option Pricing within the Uncertain Volatility Model

ArXiv ID: 2407.13213 “View on arXiv”

Authors: Unknown

Abstract

This paper explores the application of Machine Learning techniques for pricing high-dimensional options within the framework of the Uncertain Volatility Model (UVM). The UVM is a robust framework that accounts for the inherent unpredictability of market volatility by setting upper and lower bounds on volatility and the correlation among underlying assets. By integrating advanced Machine Learning algorithms, we aim to enhance the accuracy and efficiency of option pricing under the UVM, especially when the option price depends on a large number of variables, such as in basket or path-dependent options. In this paper, we consider two approaches based on Machine Learning. The first one, termed GTU, evolves backward in time, dynamically selecting at each time step the most expensive volatility and correlation for each market state. Specifically, it identifies the particular values of volatility and correlation that maximize the expected option value at the next time step, and therefore, an optimization problem must be solved. This is achieved through the use of Gaussian Process regression, the computation of expectations via a single step of a multidimensional tree and the Sequential Quadratic Programming optimization algorithm. The second approach, referred to as NNU, leverages neural networks and frames pricing in the UVM as a control problem. Specifically, we train a neural network to determine the most adverse volatility and correlation for each simulated market state, generated via random simulations. The option price is then obtained through Monte Carlo simulations, which are performed using the values for the uncertain parameters provided by the neural network. The numerical results demonstrate that the proposed approaches can significantly improve the precision of option pricing particularly in high-dimensional contexts.

Keywords: Uncertain Volatility Model, Machine Learning, Gaussian Process, Neural Networks, High-Dimensional Options, Derivatives (Options)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematics including PDEs (BSB equation), Gaussian Processes, Sequential Quadratic Programming, and stochastic control theory, indicating high complexity. While it discusses numerical results and Monte Carlo simulations, the summary focuses on theoretical algorithm development without mentioning specific backtests, datasets, or real-world implementation details, suggesting lower empirical rigor.

  flowchart TD
    A["Research Goal: Enhance High-Dim Option Pricing in UVM"] --> B{"Methodology Selection"}
    B --> C["Approach 1: GTU<br>Backward Evolution"]
    B --> D["Approach 2: NNU<br>Neural Control Problem"]
    
    C --> E["Process: Gaussian Process + Optimization"]
    D --> F["Process: Neural Network Training + Monte Carlo"]
    
    E --> G["Key Outcome: Improved Accuracy & Efficiency"]
    F --> G
    
    subgraph Inputs ["Data & Model Inputs"]
        H["High-Dim Options"]
        I["UVM Volatility & Correlation Bounds"]
    end
    
    Inputs --> B