Option pricing for Barndorff-Nielsen and Shephard model by supervised deep learning

ArXiv ID: 2402.00445 “View on arXiv”

Authors: Unknown

Abstract

This paper aims to develop a supervised deep-learning scheme to compute call option prices for the Barndorff-Nielsen and Shephard model with a non-martingale asset price process having infinite active jumps. In our deep learning scheme, teaching data is generated through the Monte Carlo method developed by Arai and Imai (2024). Moreover, the BNS model includes many variables, which makes the deep learning accuracy worse. Therefore, we will create another input variable using the Black-Scholes formula. As a result, the accuracy is improved dramatically.

Keywords: Deep Learning, Option Pricing, Barndorff-Nielsen and Shephard (BNS) Model, Monte Carlo Simulation, Black-Scholes Model

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic calculus and Lévy processes for the BNS model, requiring deep mathematical formalism. However, it demonstrates strong empirical rigor by implementing Monte Carlo simulations for data generation, using Sobol sequences for quasi-random sampling, and reporting computational speed improvements (100x faster) in a deep learning framework.

  flowchart TD
    A["Research Goal: Compute BNS Call Option Prices via Supervised Deep Learning"] --> B["Generate Training Data<br>Monte Carlo Simulation Arai & Imai (2024)"]
    B --> C{"Input Variables"}
    C --> D["BNS Model Variables<br>High Dimensionality Issue"]
    C --> E["Black-Scholes Formula Input<br>Created to Improve Accuracy"]
    D & E --> F["Computational Process<br>Supervised Deep Learning Training"]
    F --> G["Key Findings<br>Dramatic Accuracy Improvement<br>Effective Option Pricing"]