Robust and Fast Bass local volatility

TL;DR

This paper introduces a robust and efficient method for the Bass Local Volatility Model that improves the construction of state price densities and enhances numerical convolution techniques for better option pricing accuracy.

Contribution

It proposes a novel approach combining local quadratic estimation with lognormal mixture tails and demonstrates superior computational efficiency over existing methods.

Findings

Outperforms Gauss-Hermite quadrature in numerical convolutions

Effective in standard option pricing models

Validated through a detailed market case study

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.