金融工程研究中心学术报告:Explicit Approximations for Diffusion Processes and Financial Applications

报告人:南京大学 杨念 助理教授

  2019124日(星期三)上午10:30

  :览秀楼105学术报告厅

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Diffusion processes are widely used in finance such as asset pricing, derivative pricing, and term structure modeling. The use of diffusion processes in practice requires analytical tractability of these models. The explicit formula of the transition density of a diffusion process, which is in general not available, lies at the heart of the analytical tractability. In this talk, I will present two new methods, which can yield explicit approximations for transition densities of multivariate diffusions: (i) the Ito-Taylor (delta) expansion, in which the explicit density approximation is obtained via the Ito-Taylor expansion of the conditional expectation of the Dirac delta function; (ii) the Hermite expansion, the explicit density approximation of which is derived by extending the Hermite method of Ait-Sahalia (2002) to irreducible diffusions. Then I will show that the Hermite expansion, the Ito-Taylor (delta) expansion, and the pathwise expansion (Li, 2013) lead to the same expansion formulas, whereas the Hermite expansion is the bridge to show the equivalence of the latter two. Finally, I will present two important applications.  The obtained density approximations are used to (i) carry out the maximum likelihood estimation for the diffusions with discretely observed data; (ii) derive explicit expansion formulas for European option prices under irreducible diffusions. Extensive numerical experiments are also presented to demonstrate the accuracy and effectiveness of two approaches.

报告人简介:

杨念现任南京大学商学院金融与保险学系助理教授,于2013年获得香港中文大学系统工程与工程管理学系哲学(金融工程)博士学位。他的研究兴趣主要集中的金融衍生品市场、金融计量、金融合约理论等领域,其相关研究成果发表在Journal of Econometrics, Journal of Economic Dynamics and Control, Quantitative Finance等杂志。

 

 

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