Single- and Multilevel Quadrature with Error Control for Fourier Pricing under the Rough Heston Model

Battle Count: 74

Highly relevant for quantitative finance practitioners working with rough volatility models. The paper provides substantial computational savings (multilevel method achieves O(ε^{-β/p}) vs O(ε^{-(β/p+2/s_SL)}) for single-level), directly impacting calibration speed and real-time pricing. The comparison with BL2 Markovian approximation shows the direct fractional Riccati approach can be faster. Particularly relevant for desks pricing and hedging options under rough Heston dynamics.

High implementation complexity due to: (1) fractional Adams predictor-corrector scheme for the Riccati-Volterra equation, (2) scaled Gauss-Laguerre quadrature with adaptive scaling, (3) multilevel telescoping decomposition with level-dependent quadrature allocation, (4) Richardson-based error estimation for level selection, (5) root-exponential quadrature error fitting, (6) constrained optimization for damping parameter selection. Requires expertise in fractional calculus, numerical quadrature, and stochastic volatility modeling.

The paper provides detailed algorithmic descriptions, parameter sets (EuRos, SPY), damping selection procedures, and references to the BL2 implementation repository. However, the core code for the multilevel Fourier pricing method is not explicitly provided. Parameter selection involves heuristic choices (damping, scaling) that may require tuning. The fractional Adams scheme is standard and well-documented in prior literature.