Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T19:55:25.807Z Has data issue: false hasContentIssue false
  • English
  • Français

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:shuhua55@126.com (S. H. Zhang), crysralstella@126.com (J.Wang)
*Corresponding author. Email:shuhua55@126.com (S. H. Zhang), crysralstella@126.com (J.Wang)
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Ahn, C., Opion pricing when jump risk is systematic, Math. Finance, 2 (1992), pp. 299–308.Google Scholar
[2]Ahn, C. and Thomson, H., Jump-diffusion processes and the term structure of interest rates, J. Finance, 43 (1988), pp. 155–174.Google Scholar
[3]Amin, K., Jump diffusion option valuation in discrete time, J. Finance, 48 (1993), pp. 1863–1883.Google Scholar
[4]Bakshi, G., Cao, C., and Chen, Z., Empirical performance of alternative option pricing models, J. Finance, 52 (1997), pp. 2003–2049.Google Scholar
[5]Benz, E. and Trück, S., Modeling the price dynamics of CO2 emission allowances, Energy Economics, 31 (2009), pp. 4–15.Google Scholar
[6]Black, F., The pricing of commodity contracts, J. Financial Economics, 3 (1976), pp. 167–179.Google Scholar
[7]Black, F. and Scholes, M., The pricing of options and corporate liabilities, J. Political Economy, 81 (1973), pp. 637–659.Google Scholar
[8]Carmona, R. and Hinz, J., Risk-neutral models for emission allowance prices and option valuation, Management Science, 57 (2011), pp. 1453–1468.Google Scholar
[9]Chesney, M. and Taschini, L., The endogenous price dynamics of the emission allowances: An application to CO2 option pricing, Swiss Finance Institute Research Paper, Swiss Finance Institute, Zurich, 2008.Google Scholar
[10]Church, C., Carbon Trading, Master Scinece Thesis, University of Oxford, 2009.Google Scholar
[11]Daskalakis, G., Psychoyios, D., and Markellos, R. N., Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme, J. Bank. Finance, 33 (2009), pp. 1230–1241.Google Scholar
[12]D'Halluin, Y., Forsyth, P. A., and Labahn, G., A power penalty method for American options with jump diffusion processes, Numerische Mathematik, 97 (2004), pp. 321–352.Google Scholar
[13]D'Halluin, Y., Forsyth, P. A., and Vetzal, K. R., Robust numerical methods for contingent claims under jump-diffusion processes, IMA J. Numer. Anal., 25 (2005), pp. 87–112.Google Scholar
[14]Hilliard, J. E. and Reis, J., Valuation of commodity futures and options under stochastic convenience yields, interest rates, and jump diffusion in the spot, J. Financial Economics Quant. Anal., 33 (1998), pp. 61–86.Google Scholar
[15]Kou, S. G., A jump-diffusion model for option pricing, Management Sci., 48 (2002), pp. 1086–1101.Google Scholar
[16]Merton, R. C., Option pricing when underlying stock returns are discontinuous, J. Financial Economics, 3 (1976), pp. 125–144.Google Scholar
[17]Paolella, S. M. and Taschinia, L., An econometric analysis of emission allowance prices, J. Bank. Finance, 10(32) (2008), pp. 2022–2032.Google Scholar
[18]Pham, H., Optimal stopping, free boundary, and American option in a jump-diffusion model, Appl. Math. Optim., 35 (1997), pp. 145–164.Google Scholar
[19]Rubin, J. D., A model of intertemporal emission trading, banking, and borrowing, J. Environmental Economics Management, 31 (1996), pp. 269–286.CrossRefGoogle Scholar
[20]Shreve, S. E., Stochastic Calculus and Finance, Springer: New York, 2004.Google Scholar
[21]Tillmann, M., Valuation and Hedging of Carbon-Derivatives, Institut für Numerische und Angewandte Mathematik Fachbereich Mathematik, 2008.Google Scholar
[22]Toivanen, J., Numerical valuation of European and American options under Kou's jump-diffusion model, SIAM J. Sci. Comput., 30 (2008), pp. 1949–1970.Google Scholar
[23]Uhrig-Homburg, M. and Wagner, M., Futures price dynamics of CO2 emission certificates: an empirical analysis, Working Paper, University of Karlsruhe, 2007.Google Scholar
[24]Wang, S., A novel fitted finite volume method for the Black-Scholes equation governing option pricing, IMA J. Numer. Anal., 24 (2004), pp. 699–720.Google Scholar
[25]Wilmott, P., Dewynne, J., and Howison, S., Option Pricing: Mathematical Models and Computation, Oxford Financial Press, Oxford, 1993.Google Scholar
[26]Zhang, K. and Wang, S., Pricing option under jump diffusion processes with fitted finite volume method, J. Appl. Math. Comput., 201 (2008), pp. 398–413.CrossRefGoogle Scholar
[27]Zhang, K. and Wang, S., A computational scheme for option under jump diffusion processes, J. Appl. Math. Comput., 6 (2009), pp. 110–123.Google Scholar