Using Kolmogorov equations to investigate hedging errors

Thesis

This thesis presents a study of hedging errors caused by model mis-specification, making use of a Kolmogorov forward equation with δ-function initial conditions. The method is used to calculate the probability distribution of hedging errors at maturity for a number of realistic examples. An analysis of numerical schemes used to solve the Kolmogorov forward equation is presented, making particular use of Fourier transform techniques. Much of the analysis applies to a 'toy' model which captures the main features of the hedging problem. Detailed analysis of a semi-discrete Fourier numerical method for solving the toy model problem leads to a complete description of the accuracy and stability behaviour of the scheme. The thesis also includes a novel time-change method which solves the heat equation with δ-function initial conditions, using the Crank-Nicolson method, and which demonstrates improved convergence of the scheme. The numerical analysis included in the thesis explores further aspects of Fourier transform methods applied to the analysis of Partial Differential Equations with Dirac data and variable coefficients.

Authors: Whitley, A

• DOI: 10.5287/ora-z6rk2jdmk
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford