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Modeling and Computation of CO2 Allowance Derivatives Under Jump-Diffusion Processes

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  08 July 2016

Shuhua Zhang  and
Jing Wang
Shuhua Zhang*
Affiliation:
Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100190, China
Jing Wang*
Affiliation:
Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China Department of Mathematics and Physics, Bengbu College, Bengbu, 233030, China
*
*Corresponding author. Email:[email protected] (S. H. Zhang), [email protected] (J.Wang)
*Corresponding author. Email:[email protected] (S. H. Zhang), [email protected] (J.Wang)
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Abstract

In this paper, we study carbon emission trading whose market is gaining in popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on CO2 emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

Keywords

CO2 emission allowanceoption pricingjump diffusionfitted finite volume methodpartial integro-differential equationfast Fourier transform

MSC classification

Secondary: 65M12: Stability and convergence of numerical methods 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 5 , October 2016 , pp. 827 - 846
Copyright
Copyright © Global-Science Press 2016 

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