The inverse Black-Scholes problem in Radon measures space revisited: towards a new measure of market uncertainty

Paper: arXiv 2303.16773

Authors: Nizar Riane

Abstract

In this paper, we revisit the inverse Black-Scholes model, the existence of the solution is proved in more rigorous way, and the empirical study is done using different approach based on finite element method. The article leads to a measure of incertitude in the option market.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 4.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous mathematical re-examination of the inverse Black-Scholes problem using Radon measures and finite element methods to capture market uncertainty. While mathematically dense and theoretical, its empirical validation is relatively weak and limited in practical backtesting scope.

Research Flowchart

  flowchart TD
    A[Research Goal: Revisit Inverse Black-Scholes Problem & Measure Market Uncertainty] --> B[Inputs: Option Prices & Financial Market Data]
    B --> C[Rigorous Mathematical Proof in Radon Measures Space]
    C --> D[Numerical Implementation via Finite Element Method]
    D --> E[Empirical Calibration & Validation]
    E --> F[Outcome: New Measure of Market Uncertainty / Incertitude]