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Title: Affine Jump-diffusions: Stochastic Stability and Limit Theorems
Originating Office: IAS
Speaker: Zhang, Xiaowei
Issue Date: 23-Jun-2016
Event Date: 23-Jun-2016
Group/Series/Folder: Record Group 8.15 - Institute for Advanced Study
Series 3 - Audio-visual Materials
Location: 8.15:3 EF
Notes: IAS Quantitative Finance and Fintech seminar series. IAS Quantitative Finance and Fintech Mini Workshop.
Title from slide title.
Abstract: Affine jump-diffusion (AJD) processes constitute an important class of continuous time stochastic models that are widely used in finance and econometrics. Most methods for parameter estimation (e.g. maximum likelihood estimation or generalized methods of moments) of this type of processes generally assume ergodicity in order establish consistency and asymptotic normality of the estimator. In this talk, we present several results on the stochastic stability of AJDs. We establish ergodicity of AJDs by imposing a 'mean reversion' assumption and a mild condition on the distribution of the jumps, i.e. the finiteness of a logarithmic moment. As a stronger result,exponential ergodicity is proved if the jumps have a finite moment of a positive order. In addition, we prove strong laws of large numbers and functional central limit theorems for additive functional of this class of models. These limit theorems lay solid foundation for parameter estimation methods of AJDs.
Duration: 28 min.
Appears in Series:8.15:3 - Audio-visual Materials
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