IMPROVED NUMERICAL TECHNIQUES FOR OCCUPATION-TIME DERIVATIVES AND OTHER COMPLEX FINANCIAL INSTRUMENTS

Johnson, Paul (2008) IMPROVED NUMERICAL TECHNIQUES FOR OCCUPATION-TIME DERIVATIVES AND OTHER COMPLEX FINANCIAL INSTRUMENTS. Doctoral thesis, Manchester Institute for Mathematical Sciences, The University of Manchester.

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Abstract

Occupation-time derivatives are complex barrier-type options where valuation depends on the time spent beyond the barrier by the underlying asset. This thesis presents a model for corporate bonds using an occupation-time derivative, the ParAsian option, the features of which can capture bankruptcy resolution and complex capital structure with violations of the absolute priority rule. It investigates the numerics of the problem, and proposes appropriate numerical techniques to enable accurate and rapid solutions. The model is extended to include bond conversion in a two-tier structure, which presents its own numerical problems. A new occupationtime derivative that takes into account the distance of deviations beyond the barrier is presented and solved. Using existing knowledge on the asymptotic structure, new fast and efficient techniques are created for pricing American options. A second new occupation-time derivative is proposed, combining elements of early exercise with the ParAsian option to produce the American delayed-exercise option. The numerical methods employed in this thesis are based on accurate finitedifference schemes, specifically developed and enhanced to treat the various classes of problem considered.

Item Type:	Thesis (Doctoral)
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics
Depositing User:	Dr Paul Johnson
Date Deposited:	27 Nov 2009
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1357

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