Neural option pricing for rough Bergomi model

ArXiv ID: 2402.02714 “View on arXiv”

Authors: Unknown

Abstract

The rough Bergomi (rBergomi) model can accurately describe the historical and implied volatilities, and has gained much attention in the past few years. However, there are many hidden unknown parameters or even functions in the model. In this work, we investigate the potential of learning the forward variance curve in the rBergomi model using a neural SDE. To construct an efficient solver for the neural SDE, we propose a novel numerical scheme for simulating the volatility process using the modified summation of exponentials. Using the Wasserstein 1-distance to define the loss function, we show that the learned forward variance curve is capable of calibrating the price process of the underlying asset and the price of the European-style options simultaneously. Several numerical tests are provided to demonstrate its performance.

Keywords: Rough Bergomi (rBergomi) Model, Neural SDE, Forward Variance Curve, Wasserstein Distance, Option Pricing

Complexity vs Empirical Score

• Math Complexity: 9.2/10
• Empirical Rigor: 7.1/10
• Quadrant: Holy Grail
• Why: The paper presents advanced stochastic calculus and neural SDE architectures with rigorous mathematical derivations, while also including explicit numerical experiments, performance metrics, and implementation details for the proposed mSOE scheme.

  flowchart TD
    A["Research Goal:<br>Learn Forward Variance Curve in rBergomi"] --> B{"Methodology"}
    
    B --> C["Data: Option Market Prices"]
    C --> D["Neural SDE Formulation<br>+ Modified Exponential Summation"]
    
    D --> E["Loss Function:<br>Wasserstein 1-Distance"]
    
    E --> F["Optimization<br>Simultaneous Calibration"]
    
    F --> G["Key Findings"]
    
    G --> H["Simultaneous calibration of<br>Asset Price & European Options"]
    G --> I["Efficient solver for<br>Neural SDE volatility process"]
    G --> J["Validated via<br>Multiple Numerical Tests"]