Prof. Dr. Ir. C. W. (Kees) Oosterlee

Cornelis W. Oosterlee (Utrecht University, the Netherlands)

Prof. Dr. Ir. Cornelis ("Kees") Oosterlee holds the Chair of Financial Mathematics at the Mathematical Institute of Utrecht University and currently serves as Head of the Institute.
He has been actively engaged in computational finance since 2000, contributing extensively to research on numerical methods for financial mathematics.
He is the co-author of two widely recognized textbooks, "Multigrid" (2001) and "Mathematical Modeling and Computation in Finance" (2019).
His research contributions include the development of several innovative numerical techniques in financial derivative pricing and risk management, such as the COS method for Fourier cosine expansions, the SWIFT method based on the Shannon Wavelet Inverse Fourier Transform, the Stochastic Grid Bundling Method (SGBM), the Stochastic Collocation Monte Carlo Method (SCMC), and the Seven-League (7L) scheme for efficient pricing and risk evaluation. Beyond numerical finance, his research group is actively involved in applying machine learning to finance, with a focus on optimal portfolio selection, time series analysis, and anomaly detection.
Prof. Oosterlee has led EU-funded projects on risk management in finance and insurance, working closely with industry partners. Additionally, he has contributed to several Dutch national research initiatives. He has also been a guest lecturer at renowned institutions, including Oxford University in the UK, Hitotsubashi University in Japan, and the University of A Coruña in Spain.

Title: On Fourier Methods and Machine Learning Techniques for Calibration in Computational Finance

Abstract

In this presentation, we introduce a unified framework for solving linear, semi-linear, and nonlinear partial differential equations (PDEs) using backward stochastic differential equations and Fourier cosine expansions. This approach provides an elegant and computationally efficient methodology for addressing complex mathematical models in various applications.
The focus will be on the efficient pricing of financial options using Fourier-based techniques, particularly the COS method.
We will highlight its computational advantages and its effectiveness in pricing derivatives across different asset classes.

In the latter part of the presentation, we explore the application of artificial neural networks (ANNs) in financial modeling, with a special emphasis on model calibration.
We introduce an advanced framework known as the Calibration Neural Network (CaNN) methodology, which integrates neural networks with the COS method to
achieve fast and robust calibration to market-implied volatility surfaces. This synergy significantly enhances both the speed and accuracy of model calibration.
The presentation underscores the powerful interplay between mathematical finance, numerical methods, and machine learning, offering novel insights into solving complex
problems in option pricing, risk management, and financial model calibration.