Simulaton and Calibration of One-factor and Two-factor Hull-White Models

The choice of the interest rate model allows solving important problems, such as evaluation of the financial instruments, the development of risk hedging strategies and risk control (for example, to predict the possible consequences of interest rate fluctuations for the financial market). Therefore, there is an obvious need for models that allow solving the above problems with high accuracy. The aim of the research is to study classical stochastic interest rate models, estimation techniques for their parameters and model calibration methods on various financial instruments. The introduction describes the relevance of the research, as well as its aim, object, subject, and tasks. Chapter 1 contains the literature review on the modeling of interest rate dynamics. The evolution of interest rate models is considered, as well as the basic mathematical definitions and the theorems that are used in this work. The Ornstein Uhlenbeck process used in Chapter 2 for estimating the parameters of the Hull-White model is also studied in detail. In Chapter 2 we present theoretical aspects related to the statistics for stochastic differential equations: approaches to the discretization of SDEs, the application of Maximum Likelihood Estimation and Method of Moments for estimating parameters of SDEs are examined, as well as the statistical properties of their estimates. Chapter 3 deals with calibration methods of the particular case of interest rate models, namely one-factor and two-factor Hull-White models. The use of the Kalman filter approach for calibrating the Hull-White models on zero-coupon bonds has been studied. Calibration techniques on swaptions are also taken into consideration. Chapter 4 consists of simulation results for different stochastic processes, estimation of model parameters (using MLE) and calibration of models. Implementation of the Kalman Filter techniques to model calibration is shown using the example zero-coupon bond yield. Model calibration method on the swaption prices data is also considered. A comparative analysis of the results is carried out.