Date of Award
Doctor of Philosophy
This thesis is concerned with the nonparametric estimation of continuous-time stochastic processes and its applications in financial economics. It consists of three closely related chapters, two on the nonparametric estimation and Monte Carlo simulation of diffusion processes, and one on the term structure of interest rates and nonparametric pricing of derivative securities.;Chapter 1 proposes a nonparametric identification and estimation procedure for an Ito diffusion process based on discrete sampling observations. The nonparametric kernel estimator for the diffusion function developed in this chapter deals with general Ito diffusion processes and avoids any functional form specification for either the drift function or diffusion function. It is shown that under certain regularity conditions, the nonparametric diffusion function estimator is pointwise consistent and asymptotically follows a normal mixture distribution. Under stronger conditions, a consistent nonparametric estimator of the drift function is also derived based on the diffusion function estimator and the marginal density of the process. An application of the nonparametric technique to a short-term interest rate model involving Canadian daily three-month treasury bill rates is also undertaken. The estimation results provide evidence for rejecting the common parametric or semiparametric specifications for both the drift and diffusion functions.;Chapter 2 performs a Monte Carlo experiment to study the finite sample properties of the nonparametric diffusion function and drift function estimators, proposed in Chapter 1, by comparing their performance with other commonly used estimators, such as MLE, OLS, NLS, or GMM, etc., for those diffusion processes with explicit transitional density functions. It is noted from the Monte Carlo simulation results that both the nonparametric diffusion function and drift function estimators perform extremely well in these comparisons and the nonparametric drift function estimator performs much better than other estimators.;Chapter 3 extends both the traditional spot interest rate model and the interest rate derivative security pricing formulation through nonparametric specification of the diffusion function, the drift function and the market price of risk function. A procedure to obtain nonparametric prices of interest rate derivative securities by solving the valuation partial differential equation (PDE) numerically are proposed. The model is implemented using observed Canadian interest rate term structure data. Nonparametric bond and bond option prices are computed and compared with those calculated under alternative parametric models. The empirical results not only provide further evidence that the traditional spot interest rate models are misspecified, but also provide more financial market relevant information.
Jiang, George J., "Nonparametric Estimation Of Ito Diffusions With Applications To The Pricing Of Derivative Securities" (1996). Digitized Theses. 2678.