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Language:
The seminar will be in English, if there is at least one non-German speaking participant.
Field:
Applied Mathematics, Stochastics
Description of the seminar:
The stochastic volatility model is a frequently used model in modern econometrics. In the last decades many authors introduced several different notion of volatility to model their believes in the underlying economically phenomenons. In this seminar we will focus on the statistical inferences on these models and the naturally occurying dependency structures on the data.
Stochastic volatility models as hidden Markov models and statistical applications (Genon-Catalot, Jeantheau, Laredo, 2 talks )
Nonparametric statistics
Kernel deconvolution of stochastic volatility models (Comte, 2 talks )
Nonparametric volatility density estimation (Van Es, Spreij, Van Zanten, 1 talk )
Penalized projection estimator for volatility density (Comte, Genon-Catalot 2 talks )
Nonparametric estimation for a stochastic volatility model (Comte, Genon-Catalot, Rozenholc, 2 talks )
Each participant is expected to give a 60 minutes. A handout containing the most important definitions and results as well as short sketches of the proofs should be prepared for the other participants.
Requirements:
The seminar is for advanced Bachelor students and Master students who want to specialize in statistics and are already familiar with the topics typically covered in the lectures Probability Theory I and Statistics I.
Reference:
"Probability theory" Achim Klenke, Springer Spektrum Link to Heidi
"Limit theorems for discretely observed stochastic volatility models" Genon-Catalot, Jeantheau, Laredo, 1998Link to PDF
"Parameter estimation for discretely observed stochastic volatility models" Genon-Catalot, Jeantheau, Laredo, 1999Link to PDF
"Stochastic volatility models as hidden Markov models and statistical applications" Genon-Catalot, Jeantheau, Laredo, 2000Link to PDF
"Kernel deconvolution of stochastic volatility models" Comte, 2001Link to PDF
"Nonparametric volatility density estimation" Van Es, Spreij, Van Zanten, 2003Link to PDF
"Penalized projection estimator for volatility density" Comte, Genon-Catalot, 2006Link to PDF
"Nonparametric estimation for a stochastic volatility model" Comte, Genon-Catalot, Rozenholc 2007Link to PDF