Robust and Fast Bass local volatility

2024-11-06

AI Summary

The Bass local volatility (LV) model faces accuracy and efficiency bottlenecks in state price density (SPD) construction and numerical convolution-based fixed-point solving. Method: We propose a robust, efficient modeling framework: (i) for SPD estimation, we introduce the first joint use of local quadratic kernel smoothing and lognormal mixture tails—eliminating cross-maturity interpolation; (ii) for convolution acceleration, we replace Gauss–Hermite quadrature with the trapezoidal rule and integrate fixed-point iteration with marginal distribution reconstruction. Contribution/Results: Theoretical analysis and empirical validation demonstrate substantial improvements in robustness and computational speed. The framework achieves high pricing accuracy for vanilla options and real-market data while maintaining real-time feasibility. It establishes a scalable, numerically stable paradigm for practical deployment of the Bass-LV model, overcoming longstanding limitations in both calibration stability and runtime performance.

Technology Category

• Search and Optimization: Local Search
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

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.

Problem

• Eliminate interpolation need in Bass-LV model
• Improve state price density construction accuracy
• Enhance computational efficiency in numerical convolutions

Innovation

• Combines local quadratic estimation and lognormal tails
• Uses trapezoidal rule for efficient numerical convolutions
• Eliminates interpolation between maturities in volatility model