Theoretical and Empirical Validation of Heston Model

ArXiv ID: 2409.12453 “View on arXiv”

Authors: Unknown

Abstract

This study focuses on the application of the Heston model to option pricing, employing both theoretical derivations and empirical validations. The Heston model, known for its ability to incorporate stochastic volatility, is derived and analyzed to evaluate its effectiveness in pricing options. For practical application, we utilize Monte Carlo simulations alongside market data from the Crude Oil WTI market to test the model’s accuracy. Machine learning based optimization methods are also applied for the estimation of the five Heston parameters. By calibrating the model with real-world data, we assess its robustness and relevance in current financial markets, aiming to bridge the gap between theoretical finance models and their practical implementations.

Keywords: Heston Model, Monte Carlo Simulation, Option Pricing, Stochastic Volatility, Parameter Estimation, Commodities (Energy)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper presents extensive stochastic calculus and derivations for the Heston model PDE and Fourier transform solution, indicating high mathematical density, while it also includes Monte Carlo simulation implementations, calibration to real-world WTI market data, and comparisons of convergence rates, demonstrating substantial empirical validation efforts.

  flowchart TD
    A["Research Goal: Validate Heston Model for Option Pricing<br>in Commodities Market"] --> B["Methodology: Derivation & Empirical Analysis"]
    B --> C["Data Input: Crude Oil WTI Market Data"]
    C --> D["Computational Process:<br>Monte Carlo Simulation & ML Optimization"]
    D --> E["Process: Calibration of 5 Heston Parameters"]
    E --> F["Outcome: Theoretical & Empirical Validation"]
    F --> G["Outcome: Bridged Theory & Practice<br>Assessed Model Robustness"]