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Numerical solutions of Weather Derivatives and other incomplete market problems

Broni-Mensah, Edwin

[Thesis]. Manchester, UK: The University of Manchester; 2012.

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Abstract

The valuation of weather derivatives is complex since the underlying temperature process has no negotiable price. This thesis introduces a selection of models for the valuation of weather derivative contracts, governed by a stochastic underlying temperature process.We then present a new weather pricing model, which is used to determine the fair hedging price of a weather derivative under the assumptions of mean self-financing. This model is then extended to incorporate a compensation (or market price of risk) awarded to investors who hold undiversifiable risks. This results in the derivation of a non-linear two-dimensional PDE, for which the numerical evaluation cannot be performed using standard finite-difference techniques.The numerical techniques applied in this thesis are based on a broad range of lattice based schemes, including enhancements to finite-differences, quadrature methods and binomial trees. Furthermore simulations of temperature processes are undertaken that involves the development of Monte Carlo based methods.

Bibliographic metadata

Type of resource:
Content type:
Form of thesis:
Type of submission:
Degree type:
Doctor of Philosophy
Degree programme:
PhD Mathematical Sciences
Publication date:
Location:
Manchester, UK
Total pages:
282
Abstract:
The valuation of weather derivatives is complex since the underlying temperature process has no negotiable price. This thesis introduces a selection of models for the valuation of weather derivative contracts, governed by a stochastic underlying temperature process.We then present a new weather pricing model, which is used to determine the fair hedging price of a weather derivative under the assumptions of mean self-financing. This model is then extended to incorporate a compensation (or market price of risk) awarded to investors who hold undiversifiable risks. This results in the derivation of a non-linear two-dimensional PDE, for which the numerical evaluation cannot be performed using standard finite-difference techniques.The numerical techniques applied in this thesis are based on a broad range of lattice based schemes, including enhancements to finite-differences, quadrature methods and binomial trees. Furthermore simulations of temperature processes are undertaken that involves the development of Monte Carlo based methods.
Thesis main supervisor(s):
Thesis advisor(s):
Language:
en

Institutional metadata

University researcher(s):

Record metadata

Manchester eScholar ID:
uk-ac-man-scw:161717
Created by:
Broni-Mensah, Edwin
Created:
28th May, 2012, 05:29:23
Last modified by:
Broni-Mensah, Edwin
Last modified:
19th June, 2012, 13:01:23

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