Realized Local Volatility Surface

ArXiv ID: 2504.15626 “View on arXiv”

Authors: Unknown

Abstract

For quantitative trading risk management purposes, we present a novel idea: the realized local volatility surface. Concisely, it stands for the conditional expected volatility when sudden market behaviors of the underlying occur. One is able to explore risk management usages by following the orthotical Delta-Gamma dynamic hedging framework. The realized local volatility surface is, mathematically, a generalized Wiener measure from historical prices. It is reconstructed via employing high-frequency trading market data. A Stick-Breaking Gaussian Mixture Model is fitted via Hamiltonian Monte Carlo, producing a local volatility surface with 95% credible intervals. A practically validated Bayesian nonparametric estimation workflow. Empirical results on TSLA high-frequency data illustrate its ability to capture counterfactual volatility. We also discuss its application in improving volatility-based risk management.

Keywords: Realized Local Volatility, Hamiltonian Monte Carlo, Stick-Breaking Gaussian Mixture, Bayesian Nonparametrics, Dynamic Hedging, Equities / Volatility

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques including stochastic calculus (Ito’s lemma), Hamiltonian Monte Carlo for Bayesian nonparametric estimation, and a Stick-Breaking Gaussian Mixture Model, justifying a high math score. It is backtest-ready, using high-frequency TSLA data and providing practical workflows with credible intervals, warranting a strong empirical rigor score.

  flowchart TD
    A["Research Goal<br>Quantify conditional expected volatility<br>for dynamic hedging"] --> B{"Data Input:<br>High-Frequency TSLA Prices"}
    B --> C["Model Specification<br>Stick-Breaking Gaussian Mixture Model"]
    C --> D["Computational Process<br>Hamiltonian Monte Carlo HMC"]
    D --> E["Posterior Estimation<br>Bayesian Nonparametric Workflow<br>95% Credible Intervals"]
    E --> F["Outcome:<br>Realized Local Volatility Surface"]
    F --> G["Application:<br>Risk Management &<br>Delta-Gamma Dynamic Hedging"]