PhD Defense Emil S. Jørgensen
Title:Diffusion Models Observed at High Frequency and Applications in Finance
Abstract:
My thesis contains three research papers on statistical methods for discretely observed diffusion processes in finance. Emphasis is on asymptotic theory, especially within the framework of estimating functions.
The first paper is a study of high-frequency asymptotics for prediction-based estimating functions with discretely observed diffusion models and is joint work with my PhD advisor, Michael Sørensen. As our main contribution, we establish limit theorems for functionals of ρ-mixing diffusion processes and apply the results to derive existence of a consistent and asymptotically normal estimator for a tractable class of estimating functions.
The second paper contains an extension of our asymptotic results of the first paper to the case of discretely observed integrated diffusion processes. The extension relies on expansion results for functionals of diffusion and integrated diffusion processes. Integrated diffusions are of apparent interest in finance, where realized volatility or variations thereof are often used to construct a trajectory of the latent integrated volatility.
The final paper deals with the construction of a parametric class of time-changed diffusion models aimed at modeling of diversified stock indices. The models are driven by a single Brownian motion that models the non-diversifiable risk of the underlying market. Focus is on relevant statistical problems related to the model construction and, in particular, we consider estimation of the parameters and construct a simulation-based nonparametric test for the implicit one-factor hypothesis for a large class of continuous Itô semimartingales with stochastic volatility.
Supervisor: Prof. Michael Sørensen, Math, University of Copenhagen
Assessment committee:
Prof. Helle Sørensen (Chairman), MATH, University of Copenhagen
Reader. Almut Varaart , Imperial College, London
Prof. Arnaud Gloter, Université d’Evry Val d’Essonne