Fourier Pricing

An Efficient Calibration Framework for Volatility Derivatives under Rough Volatility with Jumps ArXiv ID: 2510.19126 “View on arXiv” Authors: Keyuan Wu, Tenghan Zhong, Yuxuan Ouyang Abstract We present a fast and robust calibration method for stochastic volatility models that admit Fourier-analytic transform-based pricing via characteristic functions. The design is structure-preserving: we keep the original pricing transform and (i) split the pricing formula into data-independent inte- grals and a market-dependent remainder; (ii) precompute those data-independent integrals with GPU acceleration; and (iii) approximate only the remaining, market-dependent pricing map with a small neural network. We instantiate the workflow on a rough volatility model with tempered-stable jumps tailored to power-type volatility derivatives and calibrate it to VIX options with a global-to-local search. We verify that a pure-jump rough volatility model adequately captures the VIX dynamics, consistent with prior empirical findings, and demonstrate that our calibration method achieves high accuracy and speed. ...

Fast and explicit European option pricing under tempered stable processes ArXiv ID: 2510.01211 “View on arXiv” Authors: Gaetano Agazzotti, Jean-Philippe Aguilar Abstract We provide series expansions for the tempered stable densities and for the price of European-style contracts in the exponential Lévy model driven by the tempered stable process. These formulas recover several popular option pricing models, and become particularly simple in some specific cases such as bilateral Gamma process and one-sided TS process. When compared to traditional Fourier pricing, our method has the advantage of being hyperparameter free. We also provide a detailed numerical analysis and show that our technique is competitive with state-of-the-art pricing methods. ...

A semi-Lagrangian $ε$-monotone Fourier method for continuous withdrawal GMWBs under jump-diffusion with stochastic interest rate ArXiv ID: 2310.00606 “View on arXiv” Authors: Unknown Abstract We develop an efficient pricing approach for guaranteed minimum withdrawal benefits (GMWBs) with continuous withdrawals under a realistic modeling setting with jump-diffusions and stochastic interest rate. Utilizing an impulse stochastic control framework, we formulate the no-arbitrage GMWB pricing problem as a time-dependent Hamilton-Jacobi-Bellman (HJB) Quasi-Variational Inequality (QVI) having three spatial dimensions with cross derivative terms. Through a novel numerical approach built upon a combination of a semi-Lagrangian method and the Green’s function of an associated linear partial integro-differential equation, we develop an $ε$-monotone Fourier pricing method, where $ε> 0$ is a monotonicity tolerance. Together with a provable strong comparison result for the HJB-QVI, we mathematically demonstrate convergence of the proposed scheme to the viscosity solution of the HJB-QVI as $ε\to 0$. We present a comprehensive study of the impact of simultaneously considering jumps in the sub-account process and stochastic interest rate on the no-arbitrage prices and fair insurance fees of GMWBs, as well as on the holder’s optimal withdrawal behaviors. ...