Modelling multivariate risk
Subtitle: applications to term structure and derivative pricing
By: Razvan Dorin Sufana.
Published: 2006
Language: eng
Number of pages: 182
ISBN-13: 9780494157992
Description: Chapter one introduces a multivariate process of stochastic positive semidefinite matrices, called the Wishart autoregressive (WAR) process, and considers it as a dynamic model for stochastic volatility matrices. The process is a multivariate extension of the Cox-lngersoll-Ross process and has a number of attractive features: it is an affine process, provides closed-form formulas for nonlinear forecasting at any horizon, is invariant with respect to portfolio aggregation, can be formulated in discrete time or in continuous time. The Wishart process also admits factor representations, which lead to a reduction in the number of parameters. For illustration, the process is estimated from a sequence of intraday realized volatility-covolatility matrices.Chapter two extends to the multiasset framework the closed-form solution for options with stochastic volatility derived by Heston (1993). The multivariate extension introduces a risk premium in the return equation and considers a Wishart process for the dynamics of the stochastic volatility matrix. The multivariate model is an affine model with the special property that the Laplace transform (moment generating function) of the joint process of asset returns and volatility admits a closed-form solution. This solution is the basis for pricing derivatives written on more than one asset. The approach is used to extend Merton's model (Merton (1974)) for corporate default to a framework with stochastic liability, stochastic volatility and several firms.Chapter three reveals that the class of affine term structure models introduced by Duffie and Kan (1996) is larger than previously considered in the literature. Wishart quadratic term structure models are defined based on a Wishart process of fundamental risk factors. In this framework, we derive very simple parameter restrictions to ensure positive bond yields at all maturities and observe that the usual constraint that the volatility matrix of an affine process be diagonal up to a path independent linear invertible transformation can be considerably relaxed. The Wishart Quadratic term structure model is an extension of the univariate Cox-Ingersoll-Ross model and of the quadratic models introduced in the literature. (Abstract shortened by UMI.)
Notes: Source: Dissertation Abstracts International, Volume: 67-06, Section: A, page: 2264.

Thesis (Ph.D.)--University of Toronto, 2006.

Electronic version licensed for access by U. of T. users.