主 题：Quasi-Monte Carlo methods in computational finance: An overview and some recent advances
内容简介：Quasi-Monte Carlo (QMC) methods are important numerical tools in computational finance. In this presentation, we provide an overview of this method, with particular focus on its application to computational finance. In the second part of the presentation, we describe ways of enhancing QMC. Typically, path generation methods (PGMs) such as those based on the Brownian bridge (BB), principal component analysis (PCA), and linear transformation (LT) are common techniques for enhancing QMC. While these methods increase the efficiency of QMC by reducing the effective dimension of the underlying problem, we demonstrate that discontinuity can have an adverse effect on these methods. This calls for a significant concern as discontinuities occur naturally in pricing and hedging financial derivatives. The key to our finding is that the PGMs can change the structure of discontinuity which in turn can have a significant impact on the performance of QMC. With this insight, we develop a new ``QMC-friendly" method which specifically tailors to financial derivatives with discontinuities. Extensive numerical experiments demonstrate that the proposed method is much more efficient and much more robust than other PGMs (such as BB and PCA) for pricing exotic options with discontinuous payoff functions and for estimating options' Greeks. Extension of the proposed “QMC-friendly” method is also discussed.
报告人： Ken Seng Tan 教授
University Research Chair Professor of the University of Waterloo
地 点： 竞慧东楼302
举办单位：金融工程省重点实验室 金融学院 理学院