Essays on term structure models of interest rat

This document consists of two essays on the term structure models of interest rates. The first one is "Persistent Stochastic Volatility of Interest Rate Data: Long Memory or Short Memory?" The second one is "Nonparametric Plug-in Estimation of Derivative Price Models.".;The first essay is an empirical paper. Stochastic volatility is very important in financial theory and practice. In this paper. I use both the heuristic long memory analysis tools and the model-based investigation to check whether the persistence of interest rate volatility is due to long memory. I find that a stochastic process with a highly persistent mean can generate a highly persistent, long-memory-like, stochastic volatility through the levels effect, and this persistence generated by the levels effect is more prominent than the persistence of the autonomous long memory process.;The second essay is a theoretical paper. In this paper, I propose a new method to estimate a term structure model of interest rates. Using the derivative price observations to estimate a model is a very important problem. In the literature, we see nonlinear least squares regression based on numerically solving the partial differential equation. In this paper, I manipulate the PDE to get the unknown parameter as a function of the derivative price function, then nonparametrically estimate the price function and substitute it into the parameter function to get the parameter estimator. In this way, I do not need to solve the PDE. Using this method, I can also estimate the functional form of the underlying asset process. In this paper, I use this method to develop a nonparametric estimator of a one-dimensional instantaneous rate process through the observation of bond trading prices.