Paper: arXiv 2502.07518

Abstract

Implied volatility IV is a key metric in financial markets, reflecting market expectations of future price fluctuations. Research has explored IV’s relationship with moneyness, focusing on its connection to the implied Hurst exponent H. Our study reveals that H approaches 1/2 when moneyness equals 1, marking a critical point in market efficiency expectations. We developed an IV model that integrates H to capture these dynamics more effectively. This model considers the interaction between H and the underlying-to-strike price ratio S/K, crucial for capturing IV variations based on moneyness. Using Optuna optimization across multiple indexes, the model outperformed SABR and fSABR in accuracy. This approach provides a more detailed representation of market expectations and IV-H dynamics, improving options pricing and volatility forecasting while enhancing theoretical and pratcical financial analysis.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper features advanced mathematical concepts including fractional Brownian motion, Hurst exponents, and derivations of arbitrage-free conditions, indicating high mathematical complexity. It demonstrates strong empirical rigor by using real index data, comparing against established models (SABR, fSABR), and employing optimization (Optuna) for performance evaluation.

Research Flowchart

  flowchart TD
  A["Research Goal: Improve IV Modeling<br>by Integrating Implied Regularity"] --> B["Methodology: Develop<br>IV-H Implied Hurst Exponent Model"]
  
  B --> C["Data: Multiple Financial Indexes<br>Market-Implied Volatility & Strike Prices"]
  
  C --> D["Computational Process:<br>Optuna Optimization"]
  
  D --> E["Key Findings"]
  
  E --> F["1. H &rarr; 1/2 at Moneyness = 1<br>Market Efficiency Critical Point"]
  E --> G["2. Model Outperforms<br>SABR & fSABR in Accuracy"]
  E --> H["3. Enhanced Options Pricing<br>& Volatility Forecasting"]