Time Horizon and Uncertainty in Continuous Time Finance: Preferences for Information and Term Structure Modelling

McDonald, Stuart (2007). Time Horizon and Uncertainty in Continuous Time Finance: Preferences for Information and Term Structure Modelling PhD Thesis, School of Economics, University of Queensland.

       
Attached Files (Some files may be inaccessible until you login with your UQ eSpace credentials)
Name Description MIMEType Size Downloads
n01front_mcdonald.pdf n01front_mcdonald.pdf application/pdf 7.00MB 8
n02content_mcdonald.pdf n02content_mcdonald.pdf application/pdf 7.00MB 8
Author McDonald, Stuart
Thesis Title Time Horizon and Uncertainty in Continuous Time Finance: Preferences for Information and Term Structure Modelling
School, Centre or Institute School of Economics
Institution University of Queensland
Publication date 2007
Thesis type PhD Thesis
Abstract/Summary This thesis makes a contribution to the literature on pricing and valuation in continuous time' finance by examining the relationship between investment time horizon, uncertainty and asset valuation. Part one of ths thesis concentrates on the generalized stochastic differential utility model. The first chapter contained in this part of the thesis provides a review of the infinite horizon backward stochastic differential equation and its associated g-expectation. The g-expectation is a special class of non-linear expectation operator that preserves all properties of the classical linear expectation other than linearity. The results reviewed in this chapter are then used in the second chapter of part one to construct an infinite horizon extension of the generalized stochastic differential utility model. This model is then used to formulate an infinite horizon theory of preferences for information, which focuses on the idea of non-indifference to the inter-temporal resolution of consumption risk when investment time horizon is also unknown. In this approach a preference for the early resolution of uncertainty is defined as a preference for a finer information filtration on a given consumption process. A preference for the late resolution of uncertainty is then defined as a preference for a finer information filtration on a given consumption process, which in turn leads to a definition of information neutrality or indifference to information. Based on this definition an optional stopping theorem is constructed which, based on the properties of the g-expectation operator, provides sufficient conditions for information neutrality or indifference to information in finite time. Part two of this thesis focuses on the application of stochastic partial differential equations for modeling interest rate term structure. The first chapter contained in this part of the thesis develops a new technique for simulating the stochastic partial differential equations. This technique extends to stochastic environments a numerical procedure for solving deterministic partial differential equations known as the method of lines. The first chapter contained in this part of the thesis develops the method of lines technique and provides a proof that it can be applied to solve boundary value problems associated with the linear elliptic and parabolic stochastic partial differential equations. The second chapter uses the method of lines to simulate the term structure of interest for models in which the forward rate dynamics of the zero coupon bond are defined in terms of a boundary value problem of a stochastic partial differential equation. Two forward rate models are simulated. In the first model, the forward rates follow a generalized Ornstein-Uhlenbeck process. In the second model the forward rates are assumed to follow an integrated generalized Ornstein-Uhlenbeck process. Numerical simulations of the forward rate processes for these two models point to an important role for numerical experiments in complementing theoretical developments in finance. Firstly, in both models the simulations show an unusual relationship between the forward rate and volatility: when the volatility term increases, the amount of volatility in the forward rate decreases. This indicates, for both models, that noise can be used to stabilize the stochastic partial differential equation. This phenomenon is known as stochastic resonance and is a known means of controlling unstable deterministic differential equations. In the second model, which is based on the integrated Ornstein-Uhlenbeck process, there is a diffusion constant that influences the curvature of the yield curve. Numerical experiments show that when this constant becomes large it leads to an inversion of the yield curve.

 
Citation counts: Google Scholar Search Google Scholar
Access Statistics: 256 Abstract Views, 16 File Downloads  -  Detailed Statistics
Created: Fri, 21 Nov 2008, 15:17:18 EST