Paper: arXiv 2305.13791

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.

Complexity vs Empirical Score

  • Math Complexity: 9.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]