Paper: arXiv 2604.26151

Authors: Valentin Tissot-Daguette

Abstract

We introduce the Local Occupied Volatility (LOV) model that sits between Dupire’s local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the flexibility to capture stylized facts of volatility or fit additional instruments. This is achieved by tuning the occupation sensitivity function that quantifies the effect of path-dependent shocks on volatility. We validate the model through the joint American-European calibration of options chain on non-dividend paying stocks.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper combines sophisticated stochastic analysis, such as Markovian expansion of path-dependent SDEs and occupation time measures, with concrete implementation details including neural calibration and Least Square Monte Carlo for American options. It successfully bridges a deep theoretical formulation of path-dependent volatility with practical considerations for market-consistent pricing and numerical simulation.

Research Flowchart

  flowchart TD
    A[Goal: Enhance Option Pricing Models] --> B[Input: European Vanilla Options]
    B --> C[Method: Local Occupied Volatility Model]
    C --> D[Process: Tune Occupation Sensitivity Function]
    D --> E[Process: Joint American-European Calibration]
    E --> F[Outcome: Accurate Pricing & Capturing Volatility Stylized Facts]

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