Fast reliable pricing and calibration of the rough Heston model

ArXiv ID: 2508.15080 “View on arXiv”

Authors: Svetlana Boyarchenko, Marco de Innocentis, Sergei Levendorskiĭ

Abstract

The paper is an extended and modified version of the preprint S.Boyarchenko and S.Levendorskiĭ Correct implied volatility shapes and reliable pricing in the rough Heston model". We combine a modification of the Adams method with the SINH-acceleration method S.Boyarchenko and S.Levendorskii (IJTAF 2019, v.22) of Fourier inversion (iFT) to price vanilla options under the rough Heston model. For moderate or long maturities and strikes near spot, thousands of prices are computed in several milliseconds (ms) in Matlab on a Mac with moderate specs, with relative errors $\lesssim 10^{"-4"}$. Even for options close to expiry and far-OTM, the pricing takes a few tens or hundreds of ms. We show that, for the calibrated parameters in El Euch and Rosenbaum (Math.Finance 2019, v.29), the model implied vol surface is much flatter and fits the market data poorly; thus the calibration in op.cit. is a case of ghost calibration’’ (M.Boyarchenko and S.Levendorskiĭ, Quant. Finance 2015, v.15): numerical error and model specification error offset each other, creating an apparently good fit that vanishes when a more accurate pricer is used. We explain how such errors arise in popular iFT implementations that use fixed numerical parameters, yielding spurious smiles/skews, and provide numerical evidence that SINH acceleration is faster and more accurate than competing methods. Robust error control is ensured by a general Conformal Bootstrap principle that we formulate; the principle is applicable to many Fourier-pricing methods. We outline how this principle and our method enable accurate calibration procedures that are hundreds of times faster than approaches commonly used in the industry. Disclaimer: The views expressed herein are those of the authors only. No other representation should be attributed.

Keywords: rough Heston model, Fourier inversion (iFT), SINH-acceleration, implied volatility, option pricing, Equity Derivatives

Complexity vs Empirical Score

• Math Complexity: 9.0/10
• Empirical Rigor: 8.5/10
• Quadrant: Holy Grail
• Why: The paper presents advanced mathematical techniques including fractional calculus, conformal mappings, and spectral methods for Fourier inversion, indicating high complexity. It also demonstrates strong empirical rigor through fast numerical implementation, error control, calibration performance, and comparison with competing methods.

  flowchart TD
    A["Research Goal<br>Determine if 'ghost calibration' exists in<br>the rough Heston model and develop<br>a fast, reliable pricing method"] --> B

    subgraph B ["Key Methodology & Inputs"]
        direction LR
        B1["Data: Calibrated parameters from<br>El Euch & Rosenbaum (2019)"]
        B2["Method: Modified Adams +<br>SINH-acceleration iFT"]
        B3["Principle: Conformal Bootstrap<br>for error control"]
    end

    B --> C["Computational Process<br>Implement fast numerical solver for<br>Fourier inversion in MATLAB"]

    C --> D["Outcome 1: Pricing<br>Prices thousands of options in<br>milliseconds with ~10⁻⁴ error"]
    
    C --> E["Outcome 2: Calibration Analysis<br>Reveals 'Ghost Calibration':<br>Offsetting numerical and model errors<br>create false fit that vanishes with<br>accurate pricing"]
    
    D --> F["Outcome 3: Validation<br>SINH-acceleration is faster and more<br>accurate than competing methods"]
    
    E --> G["Conclusion<br>Enables robust calibration hundreds<br>of times faster than industry standards"]
    F --> G