Numerical solutions of Weather Derivatives and other incomplete market problems

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.

Date of Award	1 Aug 2012
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Peter Duck (Supervisor)