演讲题目：快速变换算法及其在数理金融中的应用   Fast Transform and Its Application in Mathematical Finance

演 讲 人: Prof Shijie Deng （Georgia Institute of Technology）

时    间: 2014年6月16日下午3:00-4:00

地    点：本部览秀楼105

摘    要:

We propose a general computational framework for pricing path-dependent options such as discretely monitored barrier options and American-style options under a wide class of affine jump diffusion (AJD) underlying price processes. Specifically, we apply a fast transform method to compute the convolution of a known function with a transition density function of the underlying price process. We approximate the transition density function by Fourier series expansion where the characteristic function of the transition density is either of analytic form or numerically tractable. A recursive algorithm is then developed to compute the convolution of the transition density with the conditional expectation of the option value at each valuation time.  The computational complexity of the algorithm is shown to be asymptotically optimal with order O(MN), where M is the number of monitoring or exercise times of the option, and N is the number of discretized underlying price points. The proposed algorithm is applicable to non-uniformly spaced grid points for the underlying price resulting in faster convergence than the widely used FFT. It is also easily extendable to the multi-assets options pricing problems. We illustrate the advantages of this algorithm through several examples of pricing Bermudan options, barrier options, and spread options under various underlying processes. (joint work with Jingfang Huang and Li Xu)

邓世杰 教授1999年于美国加州大 学伯克利分校工业工程与运筹学系获得博士学位，现为美国乔治亚理工大学 (Georgia Institute of Technology) 工业与系统工程学副教授。邓教授的研究领域主要涉及电力工业市场化下的市场机制设计与电力价格模型、金融工程在能源市场中的应 用、金融及能源资产定价与实物期权评估、随机建模与模拟、金融市场的风险管理等前沿问题，并广泛开展了教学和科研活动，取得了颇具影响力的成果。由于科研成果显著，邓世杰教授于2002年9月获美国国家科学基金会的杰出青年奖励基金和美国电力系统 工程研究中心研究基金等竞争力非常强的基金赞助，于2006年 被美国电器和电子工程协会 (IEEE) 晋升为高级会员。邓教授从1998年至今，多次受邀在国际能源金融会议、伯克利电力改革年会、美国运筹学及管理科学研究协会年会等重要学术年会上演讲。邓世杰教授还担任了顶级学术期刊Operations Research 的副编辑 (Associate Editor) 及其它重要学术杂志、会议的评审员，并且在美国加拿大等工业界担任过专家顾问。