SINH-Acceleration

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. ...

Alternative models for FX, arbitrage opportunities and efficient pricing of double barrier options in Lévy models ArXiv ID: 2312.03915 “View on arXiv” Authors: Unknown Abstract We analyze the qualitative differences between prices of double barrier no-touch options in the Heston model and pure jump KoBoL model calibrated to the same set of the empirical data, and discuss the potential for arbitrage opportunities if the correct model is a pure jump model. We explain and demonstrate with numerical examples that accurate and fast calculations of prices of double barrier options in jump models are extremely difficult using the numerical methods available in the literature. We develop a new efficient method (GWR-SINH method) based of the Gaver-Wynn-Rho acceleration applied to the Bromwich integral; the SINH-acceleration and simplified trapezoid rule are used to evaluate perpetual double barrier options for each value of the spectral parameter in GWR-algorithm. The program in Matlab running on a Mac with moderate characteristics achieves the precision of the order of E-5 and better in several several dozen of milliseconds; the precision E-07 is achievable in about 0.1 sec. We outline the extension of GWR-SINH method to regime-switching models and models with stochastic parameters and stochastic interest rates. ...