The Mathematical Institute, University of Oxford, Eprints Archive

Uncertain interest rate modelling

Epstein, D. (1999) Uncertain interest rate modelling. PhD thesis, University of Oxford.

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Abstract

In this thesis, we introduce a non-probabilistic model for the short-term interest rate. The key concepts involved in this new approach are the non-diffusive nature of the short rate process and the uncertainty in the model parameters. The model assumes the worst possible outcome for the short rate path when pricing a fixed-income product (from the point of view of the holder) and differs in many important ways from the traditional approaches of fully deterministic or stochastic rates. In this new model, delta hedging and unique pricing play no role, nor does any market price of risk term appear. We present the model and explore the analytical and numerical solutions of the associated partial differential equation. We show how to optimally hedge the interest rate risk of a fixed-income portfolio and price and hedge common and exotic fixed-income products. Finally, we consider extensions to the model and present conclusions and areas for further research.

Item Type:Thesis (PhD)
Subjects:O - Z > Partial differential equations
D - G > Game theory, mathematical finance, economics, social and behavioral sciences
H - N > Numerical analysis
Research Groups:Mathematical and Computational Finance Group
ID Code:35
Deposited By:Eprints Administrator
Deposited On:10 Mar 2004
Last Modified:20 Jul 2009 14:18

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