Doctoral thesis

Constrained nonparametric dependence with application in finance


262 p

Thèse de doctorat: Università della Svizzera italiana, 2003 (jury note: Summa cum laude)

English The developments of financial theory in the last decades have shown that one of the most fundamental topics in Finance is the specification of dependence between different risk variables. Empirical evidence on financial time series (such as returns, interest rates, or exchange rates) as well as recent developments in risk management (such as the analysis of dependence between default risks of different borrowers or dependence between extreme risks) suggest that dependence between financial variables exhibits strong features of nonlinearity. The purpose of this thesis is to develop a new approach to nonlinear dependence which is intermediate between pure parametric and pure nonparametric specifications, combining desirable features of the two. In this approach, called constrained nonparametric dependence, the joint density is constrained and depends on a small number of one-dimensional functional parameters, that are functions of one variable. The thesis is organized in three chapters. The first chapter introduces constrained nonparametric specifications, and motivates their application in Finance. The core of the thesis consists of Chapter 2 and 3. Chapter 2 is devoted to modeling methodologies, and presents the analysis of nonlinear serial dependence in a dynamic constrained nonparametric specification by treating the case of dynamic duration models with proportional hazard. Statistical inference is considered in Chapter 3, where we provide efficient nonparametric estimators for the functional parameters characterizing nonlinear dependence.
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