教育部人文社科重点研究基地中央财经大学中国精算研究院学术活动

短期课程

(2026年11月17—18日）

主题一： Pricing options using Fast Fourier Transform under Lévy processes

摘要：This lecture presents the Fast Fourier Transform (FFT) method for pricing European options in exponential Lévy models, generalizing beyond the classical Black–Scholes framework. Starting from the Lévy–Khintchine formula and the risk-neutral setup, we derive the option price as an inverse Fourier integral of the payoff transform and the characteristic exponent. We explicitly construct the analytical continuation of the payoff transform into the complex plane, ensuring integrability, and show how the Black–Scholes model arises as a particular case. The derived pricing formula is compared with the well-known Lewis formula, highlighting their mathematical equivalence and the computational advantages of our representation for FFT implementation. Finally, we introduce data-driven characteristic functions, allowing options to be priced directly from empirical log-returns without parametric calibration of the underlying Lévy measure.

主题二： Numerical methods for computing risk measures in Lévy models

摘要：Thislecture develops numerical methods for computing the Value-at-Risk and the intra-horizon Value-at-Risk for processes driven by exponential Lévy models. Both measures are dual to option prices: the terminal-horizon measure corresponds to a European digital option, while the intra-horizon measure — the loss level exceeded with a given probability at any time within a fixed horizon — corresponds to a one-touch digital option, that is, to a first-passage probability. After a brief reminder on Lévy processes and the Wiener–Hopf factorization, the lecture presents two computational routes: recovery of the terminal distribution from the characteristic function by the Gil–Pelaez formula with the Fast Fourier Transform, and inversion of the first-passage distribution in time by the Gaver–Stehfest algorithm. A substantial part of the lecture is devoted to the spectrally negative case, natural in insurance and ruin theory, where the Wiener–Hopf factorization becomes semi-explicit: the supremum factor is exponential with rate given by the positive root of the Laplace exponent, and the infimum factor follows by division. Only one scalar nonlinear equation has to be solved, which makes the method fast and differentiable, so exact gradients of the first-passage probability are available without surrogate approximations.

主讲人：OlegKudriavtsev

Dr. Kudriavtsev is the Head of the Department of Computer Science and Customs Technologies at the Rostov Branch of Russian Customs Academy and Professor at the Institute of Mathematics, Mechanics and Computer Science of Southern Federal University and Research Director at InWise Systems, LLC. He is an expert in Computational Finance and Applied Mathematics, a member of the international research group MathRisk. Oleg Kudriavtsev holds a Degree of Doctor of Science in Physics and Mathematics (Russian analog of Habilitation Degree) from Central Economics and Mathematics Institute of Russian Academy of Science, (Moscow, Russia). The field of his research interests includes the development of fast and efficient computational algorithms for pricing path-dependent options and risk estimation in models admitting jumps (numerical Wiener-Hopf factorization, Monte Carlo methods, finite difference schemes, integral transform methods).

上课时间：

2026年11月17日（周二）上午10:00-11:00

2026年11月18日（周三）上午10:00-11:00

上课地点：

沙河校区学院楼13号楼209教室

邀 请 人：韦晓

撰稿：韦晓

审稿：王庆焕

编辑：薛丽娜

审核：马冰