The Quadratic Local Variance Gamma Model: an arbitrage-free interpolation of class C3 for option prices

ArXiv ID: 2305.13791 “View on arXiv”

Authors: Unknown

Abstract

This paper generalizes the local variance gamma model of Carr and Nadtochiy, to a piecewise quadratic local variance function. The formulation encompasses the piecewise linear Bachelier and piecewise linear Black local variance gamma models. The quadratic local variance function results in an arbitrage-free interpolation of class C3. The increased smoothness over the piecewise-constant and piecewise-linear representation allows to reduce the number of knots when interpolating raw market quotes, thus providing an interesting alternative to regularization while reducing the computational cost.

Keywords: local variance gamma model, Cubic interpolation, Arbitrage-free pricing, Piecewise quadratic, Equities

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper is dense with advanced mathematical derivations, including partial differential equations, hyperbolic functions, and tridiagonal systems, while the excerpt provides no empirical backtesting, data, or implementation details.

  flowchart TD
    A["Research Goal: Develop an Arbitrage-Free, Smooth Interpolation Method for Option Prices"] --> B["Methodology: Generalize Local Variance Gamma to Piecewise Quadratic Local Variance"]
    B --> C["Input: Raw Market Option Quotes"]
    C --> D["Computation: Apply C3-Smooth Quadratic LVG to Fit Market Data"]
    D --> E{"Outcome: Arbitrage-Free Pricing & Volatility Surfaces"}
    E --> F["Benefit: Reduced Knots & Computational Cost vs. Regularization"]