Numerical solutions of Weather Derivatives and other incomplete market problems

  • Edwin Broni-Mensah

Student thesis: Phd


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 Award1 Aug 2012
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPeter Duck (Supervisor)


  • weather derivatives
  • financial mathematics
  • computational finance
  • numerical methods

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