学院讲坛：On?Fourier?Methods?and?Machine?Learning?Techniques?in?Computational?Finance

一、讲座时间

2024年10月16日（周三）13:30

二、讲座地点

浙江工业大学屏峰校区?博易楼B303

三、讲座主题

OnFourierMethodsandMachineLearningTechniquesinComputationalFinance

四、主讲人简介

Cornelis(Kees)Oosterlee教授是乌特勒支大学担任数学学院院长和金融数学系系主任。自2000年以来，他一直致力于金融数学领域的计算问题研究。他是两本英文教科书的合著者：2001年出版的《多重网格》2019年出版的《金融数学模型与计算》，并发表了众多学术论文。上述第二本书最近已被翻译成中文出版。

Oosterlee教授共同开发的金融衍生品定价和风险管理方法包括基于傅里叶余弦展开的COS方法、Shannon?Wavelet?Inverse?Fourier?Transform?method?(香农小波逆傅里叶变换方法)、Stochastic?Grid?Bundling?Method?(随机网格捆绑方法)、Stochastic?Collocation?Monte?Carlo?Method?(随机配置蒙特卡罗方法)和Seven-League格式(7L)。金融机器学习是Oosterlee研究组的另一个研究兴趣，他在这一领域致力于最优投资组合选择、时间序列和异常检测方法的研究。Oosterlee教授曾领导两个与业界合作的欧盟金融和保险风险管理项目，他还支持了几个荷兰国家级项目。他曾在英国牛津大学、日本一桥大学、西班牙科鲁尼亚大学等多所大学担任客座讲师。

五：讲座摘要

In?this?presentation,?we?explore?the?integration?of?Fourier?methods?and?machine?learning?techniques?in?computational?finance,?focusing?on?the?pricing?of?financial?derivatives.?We?begin?by?revisiting?the?COS?method,?a?Fourier-cosine?expansion?technique,?as?a?fast?and?accurate?method?for?option?valuation,?leveraging?characteristic?functions?of?asset?price?processes.?We?demonstrate?the?computational?efficiency?of?the?COS?method,?particularly?when?applied?to?models?like?the?Heston?stochastic?volatility?model.?The?challenges?of?implied?volatility?computation?and?model?inversion?are?addressed.?To?overcome?these?challenges,?we?employ?neural?networks?to?approximate?the?pricing?function?and?its?inverse,?introducing?techniques?such?as?gradient?squashing?to?handle?steep?gradients?effectively.?The?Calibration?Neural?Network?(CaNN)?framework?is?presented,?combining?the?COS?method?with?neural?networks?to?accelerate?option?pricing?and?model?calibration.?We?showcase?how?the?CaNN?approach?significantly?reduces?computational?time?while?maintaining?high?accuracy,?making?it?suitable?for?real-world?financial?engineering?tasks.?This?collaborative?work?with?Shuaiqiang?Liu,?Sander?Bohte,?Anastasia?Borovykh,?demonstrates?the?synergy?between?advanced?numerical?methods?and?machine?learning?in?addressing?computational?challenges?in?finance.