Specification analysis of drift and volatility functions of the interest rate processes
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Modeling the risk-free interest rate process is very important for the pricing of fixed income securities and interest rate derivatives. Previous studies have identified two features of the short-term risk-free interest rate: nonlinear drift and stochastic volatility. However, little is known about which specification is more fundamental to characterize the dynamics of short term interest rate. In this study, I compare di‹erent models of the short rates and test whether these haracteristics are of equal importance. Chapter 1 motivates this study by listing several important empirical questions regarding the interest rate process. Chapter 2 proposes a general model that nests both nonlinear drift and stochastic volatility. It is shown that the nonlinear drift is not essential whereas stochastic volatility is indispensable for a parsimonious model of the short rates. Chapter 3 compares the popular stochastic volatility model with its regime switching counterpart. I find strong evidence of regime shifts in the short rate volatilities for four developed countries. Chapter 4 uses a PDE approach to estimate continuous-time short rate models. The results match those found with a discrete-time framework. The last chapter summarizes the empirical findings and gives directions for future research.