This thesis is concerned with the modelling of the term structure of interest rates, with a particular focus on empirical aspects of the modelling. In this thesis, we explore the ??-parameterised (?? being the length of time to maturity) term structure of interest rates, corresponding to the traditional T-parameterised (T being the time of maturity) term structure of interest rates. The constructions of Australian yield curves are illustrated using generic yield curves produced by the Reserve Bank of Australia based on bonds on issue and by constructed yield curves of the Commonwealth Bank of Australia derived from swap rates. The data used to build the models is Australian Treasury yields from January 1996 to December 2001 for maturities of 1, 2, 3, 5 and 10 years, and the second data used to validate the model is Australian Treasury yields from July 2000 to April 2004 for maturities of all years from 1-10. Both data were supplied by the Reserve Bank of Australia. Initially, univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH), with models of individual yield increment time series are developed for a set of fixed maturities. Then, a multivariate Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution of the term structure of yield increments is developed. This model captures many important properties of financial data such as volatility mean reversion, volatility persistency, stationarity and heavy tails. There are two innovations of GARCH modelling in this thesis: (i) the development of the Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution using meta-elliptical distribution in which the degrees of freedom of each series varies with maturity, and the estimation is given; (ii) the development of a GARCH model of term structure of interest rates (TS-GARCH). The TS-GARCH model describes the parameters specifying the GARCH model and the degrees of freedom using simple smooth functions of time to maturity of component series. TS-GARCH allows an empirical description of complete interest rate yield curve increments therefore allowing the model to be used for interpolation to additional maturity beyond those used to construct the model. Diagnostics of TS-GARCH model are provided using Australian Treasury bond yields.

Thesis (Ph. D.)--University of Chicago Graduate School of Business, August 1999. / Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 110-115). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 110-115). Also available on the Internet.

No description available.

This dissertation looks at various specific applications of stochastic processes in finance. The motivation for this work has been the work on the valuation of the price of an Asian option by Rogers and Shi (1995). Here, we look at functions of integrals of log - Gaussian processes to obtain approximations to the prices of various financial instruments. We look at pricing of bonds and payments contingent on the interest rate. The interest rate is assumed to be log - Gaussian, thus ensuring that it does not go negative. Obtaining the exact price might not be easy in all cases - hence we use of a combination of a conditioning argument and Jensen's inequality to obtain the lower bound to the prices of the bond as well as payments contingent on interest rates. We look at single driver models as well as multi-driver models. We also look at bonds where default is possible. We try to provide a mathematical justification for the choice of the conditioning factor used throughout the thesis to approximate the price of bonds and options. This is similar to the approach used by Rogers and Shi (1995) to valuing an Asian option; but they had provided no mathematical justification. Another part of this dissertation deals with the problem of pricing European call options on stochastically volatile assets. Further, the price and the volatility processes are in general correlated amongst themselves. Obtaining an exact price is quite involved and computation intensive. Most of the previous work in this field has been based on the solution to a system of partial differential equations. As in the case of pricing bonds, here too, we use a conditioning argument to obtain an approximation to the prices. This method is much faster and less computation intensive. We look at the situations of fixed and stochastic interest rates separately and in each case, we look at the volatility process following a simple Brownian motion and an Ornstein Uhlenbeck process. We also look at the value of stop - loss reinsurance contract for the case of a doubly stochastic Poisson process. Finally, we look at an alternative method of pricing bonds and Asian options. This is done by using a direct expansion and thus avoids the numerical integration that is used in the earlier chapters.

No description available.

No description available.

Thesis (Ph. D.)--University of Hawaii at Manoa, 1995. / Includes bibliographical references (leaves 194-210). / Microfiche. / xv, 210 leaves, bound 29 cm

This thesis is concerned with the modelling of the term structure of interest rates, with a particular focus on empirical aspects of the modelling. In this thesis, we explore the ??-parameterised (?? being the length of time to maturity) term structure of interest rates, corresponding to the traditional T-parameterised (T being the time of maturity) term structure of interest rates. The constructions of Australian yield curves are illustrated using generic yield curves produced by the Reserve Bank of Australia based on bonds on issue and by constructed yield curves of the Commonwealth Bank of Australia derived from swap rates. The data used to build the models is Australian Treasury yields from January 1996 to December 2001 for maturities of 1, 2, 3, 5 and 10 years, and the second data used to validate the model is Australian Treasury yields from July 2000 to April 2004 for maturities of all years from 1-10. Both data were supplied by the Reserve Bank of Australia. Initially, univariate Generalised Autoregressive Conditional Heteroskedasticity (GARCH), with models of individual yield increment time series are developed for a set of fixed maturities. Then, a multivariate Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution of the term structure of yield increments is developed. This model captures many important properties of financial data such as volatility mean reversion, volatility persistency, stationarity and heavy tails. There are two innovations of GARCH modelling in this thesis: (i) the development of the Matrix-Diagonal GARCH model with multivariate asymmetric t-distribution using meta-elliptical distribution in which the degrees of freedom of each series varies with maturity, and the estimation is given; (ii) the development of a GARCH model of term structure of interest rates (TS-GARCH). The TS-GARCH model describes the parameters specifying the GARCH model and the degrees of freedom using simple smooth functions of time to maturity of component series. TS-GARCH allows an empirical description of complete interest rate yield curve increments therefore allowing the model to be used for interpolation to additional maturity beyond those used to construct the model. Diagnostics of TS-GARCH model are provided using Australian Treasury bond yields.