Estimating a Realized Local Volatility Surface from High-Frequency Data

Summary

The document introduces a realized local volatility surface as a way to estimate conditional volatility during abrupt movements in an underlying asset. It frames the estimate as a generalized Wiener measure derived from historical prices and links its use to Delta-Gamma dynamic hedging for risk management.

The proposed workflow uses high-frequency market data and fits a stick-breaking Gaussian mixture model with Hamiltonian Monte Carlo. It produces a volatility surface with 95% credible intervals, intended to represent uncertainty in the estimate. The document reports an empirical illustration using TSLA data and says the method captures counterfactual volatility. It also discusses potential use in volatility-based risk management. The brief description does not define the counterfactual volatility measure, give performance comparisons, or provide details about data selection and validation, so the practical robustness of the approach cannot be assessed from this summary alone.

Key ideas

• The realized local volatility surface is intended to estimate conditional volatility during sudden market behavior.
• The method reconstructs the surface from high-frequency historical prices.
• A stick-breaking Gaussian mixture model is fitted using Hamiltonian Monte Carlo.
• The output includes 95% credible intervals to express estimation uncertainty.
• The proposed risk-management application is dynamic hedging within a Delta-Gamma framework.

Tags

# Realized Local Volatility Surface


# Realized Local Volatility Surface









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.