Paper: arXiv 2409.12453

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (19)

  1. Transform analysis and asset pricing for affine jump-diffusions (2000)
  2. Monte Carlo methods in financial engineering (2004)
  3. A closed-form solution for options with stochastic volatility with applications to bond and currency options (1993)
  4. The volatility surface: a practitioner’s guide (2011)
  5. Arbitrage-free SVI volatility surfaces (2014)
  6. The valuation of options for alternative stochastic processes (1976)
  7. Pricing American options on jump-diffusion processes using Fourier Hermite series expansions (2005)
  8. An analysis of American options (1992)
and 11 more
  1. A canonical optimal stopping problem for American options and its numerical solution (2000)
  2. Pricing American options by simulation using a stochastic mesh with optimized weights (2000)
  3. Estimating security price derivatives using simulation (1996)
  4. Option valuation under stochastic volatility ii (2009)
  5. The pricing of options and corporate liabilities (1973)
  6. Option pricing when the variance changes randomly: Theory, estimation, and an application (1987)
  7. Option values under stochastic volatility: Theory and empirical estimates (1987)
  8. The pricing of options on assets with stochastic volatilities (1987)
  9. Option pricing with random volatilities in complete markets (1994)
  10. Stock price distributions with stochastic volatility: an analytic approach (1991)
  11. Deriving Better Second-Order Derivatives (2022) — link

0 of 19 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.