Robust and Fast Bass Local Volatility
arXiv:2411.04321
The paper introduces a fast and robust method for the Bass Local Volatility model by using local quadratic estimation with lognormal mixture tails to construct risk‑neutral densities and applying trapezoidal‑rule based convolutions that outperform Gauss‑Hermite quadrature, demonstrated on standard option pricing models and a market case study.
Abstract
The Bass Local Volatility Model, as studied in {henry2021bass}, stands out for its ability to eliminate the need for interpolation between maturities. This offers a significant advantage over traditional local volatility models. However, its performance highly depends on accurate construction of risk neutral 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 risk neutral 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.