Interest rate models with non-gaussian driven stochastic volatility
Abstract
In this thesis, we consider some two-factor short rate models that incorporate
stochastic volatility with jumps. The motivation for studying such kinds of model
is to overcome the shortcomings of di usion-based stochastic models and to provide
a more accurate description of the empirical characteristics of the short rates. In
our rst model, a jump process for the short-rate volatility is described with jump
times generated by a Poisson process and with jump sizes following exponential
distribution. Secondly, we extend the volatility model further by taking a superposition
of two independent jump processes. We present the corresponding Markov
chain Monte Carlo estimation algorithm and provide estimation results of candidate
model parameters, latent volatility processes and the jump processes using the 3-
month U.S. Treasury Bill rates. Finally, we apply our models to price fixed-income
products through Monte Carlo simulation.