Robust and Fast Bass local volatility

ArXiv ID: 2411.04321 “View on arXiv”

Authors: Unknown

Abstract

The Bass Local Volatility Model (Bass-LV), as studied in [“Conze and Henry-Labordere, 2021”], stands out for its ability to eliminate the need for interpolation between maturities. This offers a significant advantage over traditional LV models. However, its performance highly depends on accurate construction of state price densities and the corresponding marginal distributions and efficient numerical convolutions which are necessary when solving the associated fixed point problems. In this paper, we propose a new approach combining local quadratic estimation and lognormal mixture tails for the construction of state price densities. We investigate computational efficiency of trapezoidal rule based schemes for numerical convolutions and show that they outperform commonly used Gauss-Hermite quadrature. We demonstrate the performance of the proposed method, both in standard option pricing models, as well as through a detailed market case study.

Keywords: Bass Local Volatility Model, State Price Densities, Numerical Convolutions, Trapezoidal Rule, Option Pricing, Equity Derivatives

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper is heavily theoretical, involving advanced PDEs, martingale optimal transport, and fixed-point algorithms, while also demonstrating performance with market case studies and detailed numerical comparisons.
  flowchart TD
    A["Research Goal<br>Enhance Bass Local Volatility Model<br>for robust and efficient pricing"] --> B["Key Methodology<br>Local Quadratic Estimation<br>Lognormal Mixture Tails"]
    B --> C["Data Inputs<br>Market Option Data<br>Implied Volatility Surfaces"]
    C --> D["Computational Processes<br>Numerical Convolution via<br>Trapezoidal Rule"]
    D --> E["Performance Benchmarking<br>vs. Gauss-Hermite Quadrature"]
    E --> F["Outcomes<br>Improved State Price Density Construction<br>Superior Computational Efficiency<br>Validated in Equity Derivatives Case Study"]
    F --> G["Conclusions<br>Trapezoidal method outperforms standard approaches<br>Robust solution for Bass-LV fixed point problems"]