Paper: arXiv 2311.07211

Abstract

In this work, we present a novel machine learning approach for pricing high-dimensional American options based on the modified Gaussian process regression (GPR). We incorporate deep kernel learning and sparse variational Gaussian processes to address the challenges traditionally associated with GPR. These challenges include its diminished reliability in high-dimensional scenarios and the excessive computational costs associated with processing extensive numbers of simulated paths Our findings indicate that the proposed method surpasses the performance of the least squares Monte Carlo method in high-dimensional scenarios, particularly when the underlying assets are modeled by Merton’s jump diffusion model. Moreover, our approach does not exhibit a significant increase in computational time as the number of dimensions grows. Consequently, this method emerges as a potential tool for alleviating the challenges posed by the curse of dimensionality.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper involves advanced mathematical concepts like Gaussian Processes, deep kernel learning, and variational inference, with detailed derivations in the theory sections. It also presents empirical experiments comparing performance against Least Squares Monte Carlo under jump diffusion models, discussing computational time and curse of dimensionality, indicating a backtest-ready approach.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Pricing High-dim American Options"] --> B["Data & Model Setup<br>Simulated Paths, Merton Jump Diffusion"]
  B --> C["Core Methodology<br>Modified Gaussian Process Regression"]
  C --> D["Key Innovations<br>Deep Kernel Learning & Sparse Variational GPs"]
  D --> E["Computational Process<br>Addressing Curse of Dimensionality"]
  E --> F["Key Findings<br>Outperforms LS Monte Carlo"]
  F --> G["Outcome<br>Scalable, Computationally Efficient"]