Machine-learning regression methods for American-style path-dependent contracts

ArXiv ID: 2311.16762 “View on arXiv”

Authors: Unknown

Abstract

Evaluating financial products with early-termination clauses, in particular those with path-dependent structures, is challenging. This paper focuses on Asian options, look-back options, and callable certificates. We will compare regression methods for pricing and computing sensitivities, highlighting modern machine learning techniques against traditional polynomial basis functions. Specifically, we will analyze randomized recurrent and feed-forward neural networks, along with a novel approach using signatures of the underlying price process. For option sensitivities like Delta and Gamma, we will incorporate Chebyshev interpolation. Our findings show that machine learning algorithms often match the accuracy and efficiency of traditional methods for Asian and look-back options, while randomized neural networks are best for callable certificates. Furthermore, we apply Chebyshev interpolation for Delta and Gamma calculations for the first time in Asian options and callable certificates.

Keywords: Monte Carlo Simulation, Neural Networks, Path-Dependent Options, Greeks (Sensitivities), Chebyshev Interpolation, Derivatives (Exotic Options)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques including randomized recurrent/feed-forward neural networks, signature methods, and Chebyshev interpolation for computing sensitivities, requiring deep theoretical understanding. It demonstrates strong empirical rigor through extensive backtesting against benchmarks (polynomial basis functions, GPR-GHQ algorithm, binomial Markov chain) across Asian, look-back options, and callable certificates, with detailed statistical uncertainty analysis and computational time tables.

  flowchart TD
    A["Research Goal:<br>Compare ML vs. Polynomial Regression<br>for Path-Dependent Options"] --> B["Inputs:<br>Monte Carlo Simulations &<br>Financial Market Data"]
    B --> C["Methodology:<br>Randomized Neural Networks<br>& Signature Methods"]
    B --> D["Methodology:<br>Chebyshev Interpolation<br>for Greeks Delta & Gamma"]
    C --> E["Computational Process:<br>Pricing Asian Options, Look-Back,<br>& Callable Certificates"]
    D --> E
    E --> F{"Key Findings/Outcomes"}
    F --> G1["ML matches accuracy/efficiency<br>for Asian & Look-Back Options"]
    F --> G2["Randomized NN best for<br>Callable Certificates"]
    F --> G3["First application of Chebyshev<br>Interpolation for Greeks in Asian &<br>Callable Certificates"]