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Two Essays in Quantitative Finance

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dc.contributor.advisor Xing, Haipeng en_US
dc.contributor.author Wang, Ke en_US
dc.contributor.other Department of Applied Mathematics and Statistics en_US
dc.date.accessioned 2017-09-20T16:52:33Z
dc.date.available 2017-09-20T16:52:33Z
dc.date.issued 2016-12-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/77343 en_US
dc.description 208 pgs en_US
dc.description.abstract This dissertation explores two interesting problems in quantitative finance. In the first part, we consider the detection methods on structural breaks that are characterized by a credit rating transition matrix based on homogeneous Markov process model. Recent studies have shown that firms' credit rating migration process is not stationary and may have structural breaks. Assuming the generator of probability transition matrices of firms' credit rating to be piecewise constant and the jump time of generator corresponds to the structural break time in the pattern of firms' rating migrations, we study several types of sequential surveillance rules for early detection. The surveillance rules we investigated includes the Shewhart control chart, an generalized likelihood ratio (GLR) detection rule for a single change-point with unknown pre- and post-change transition matrices, a detection rule based on an extension of Shiryaev's Bayes single change-point model, and a detection rule for multiple unknown structural breaks. We provide theoretical discussion and extensive simulations to compare the performance of these rules. We further use these rules to online detect structural breaks in firms' credit rating migrations based on U.S. firms' rating record from 1986 to 2012. In part two, we develop a multivariate log-linear Poisson time series model to investigate the interdependence between components of a vector time series of counts. Maximum likelihood method is used for the estimation of the parameters and the property of geometrically ergodic is demonstrated. We further successfully applied it to study the interdependence of trading behavior in high-frequency trading market and of tail exceedance events in different markets. Specifically, we generalized the univariate log-linear Poisson model for time series counts data to the multivariate case, and developed an inference procedure for it. In this study, this model has been applied to investigate two types of time series counts data in finance. The first application is to use the developed model to study the dependence of financial risks in different market. Specifically, consider the stock market indices in the US, Europe, and Japan, the exceedance of the stock index return over certain threshold represents the magnitude of market variations and provides us a new measurement for the market tail risk in different countries/market. The second application is the interdependence of trading behavior for different stocks, through which the impact of one stock's trading behavior on another stock can be quantitatively modeled and identified by this model. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Statistics -- Finance en_US
dc.subject.other credit rating transition matrix, multivariate log linear poisson model, quantitative finance, structure break detection, time series of counts en_US
dc.title Two Essays in Quantitative Finance en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Rachev, Svetlozar en_US
dc.contributor.committeemember Douady, Raphael en_US
dc.contributor.committeemember Xiao, Keli en_US


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