Type
Text
Type
Dissertation
Advisor
Xing, Haipeng | Rachev, Svetlozar | Zhu, Wei | Fang, Yixin.
Date
2013-12-01
Keywords
default risk, free-boundary problem, intensity model, option price, stochastic control, time-varying coefficients | Applied mathematics
Department
Department of Applied Mathematics and Statistics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76482
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
This dissertation research explores two interesting problems in financial econometrics. In part one, we considers the problem of pricing European options in the presence of proportional transaction costs when the underlying stock price follows a jump-diffusion process. Based on utility maximization approach, the option pricing and hedging can be reformulated as a singular stochastic control problem. And furthermore, the value functions of the problem are the solutions of a free boundary problem, in particular, a partial integro-differential equation, under different boundary conditions. And we develop a coupled backward induction algorithm which is based on the connection between the free boundary problem and optimal stopping problem. And numerical examples are also provided. In part two, we focus on the dynamics of default risk with stochastic covariates in the presence of structural breaks. We consider a Cox type intensity model which is a classic model in survival analysis to deal with the counting process. Since it is widely used to to analyze the dynamics of default of firms to the effect of possible stochastic covariate processes. We assume there are multiple unknown structural breaks in the regression coefficients and we develop an estimation procedure for the regression coefficients and structural break points, which combines recent developments in estimating equations for counting process and inference on multiple structural breaks. | 151 pages
Recommended Citation
Yu, Yang, "Two Essays in Financial Econometrics" (2013). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2397.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2397