Volatility models in practice: Rough, Path-dependent or Markovian?

ArXiv ID: 2401.03345 “View on arXiv”

Authors: Unknown

Abstract

We present an empirical study examining several claims related to option prices in rough volatility literature using SPX options data. Our results show that rough volatility models with the parameter $H \in (0,1/2)$ are inconsistent with the global shape of SPX smiles. In particular, the at-the-money SPX skew is incompatible with the power-law shape generated by these models, which increases too fast for short maturities and decays too slowly for longer maturities. For maturities between one week and three months, rough volatility models underperform one-factor Markovian models with the same number of parameters. When extended to longer maturities, rough volatility models do not consistently outperform one-factor Markovian models. Our study identifies a non-rough path-dependent model and a two-factor Markovian model that outperform their rough counterparts in capturing SPX smiles between one week and three years, with only 3 to 4 parameters.

Keywords: Rough Volatility, SPX Options, Hurst Parameter, Volatility Smile, Markovian Models, Equity Index Options

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts such as fractional Brownian motion and Volterra processes, and includes extensive LaTeX formulas and derivations, indicating high math complexity. It also demonstrates high empirical rigor through backtesting on historical SPX options data from 2011-2022, rigorous calibration, and out-of-sample prediction assessment, comparing multiple models with quantitative metrics.

  flowchart TD
    Goal["Research Goal:<br>Empirically test claims of rough volatility<br>models using SPX options data"]
    Data["Data Input:<br>SPX Options<br>(maturities 1 week to 3 years)"]
    CompA["Compute: Global Shape & ATM Skew<br>Rough models H ∈ (0,1/2) vs. Markovian"]
    ResultA["Finding 1:<br>Rough models inconsistent with global shape.<br>Skew too fast for short maturities,<br>decays too slowly for long maturities."]
    CompB["Compare Performance:<br>Rough vs. Non-rough<br>(1-factor & 2-factor models)"]
    ResultB["Finding 2:<br>Non-rough path-dependent &<br>2-factor Markovian models outperform<br>rough models using 3-4 parameters."]
    
    Goal --> Data
    Data --> CompA
    CompA --> ResultA
    ResultA --> CompB
    CompB --> ResultB