Fitted finite volume method for pricing CO₂ futures option based on the underlying with non-log-normal distribution

References

• P. Aatola, M. Ollikainen, and A. Toppinen, Price determination in the EU ETS market: Theory and econometric analysis with market fundamentals, Energy Econ. 36 (2013), pp. 380–395. doi: 10.1016/j.eneco.2012.09.009
   Web of Science ®Google Scholar
• D.de G. Allen and R.V. Southwell, Relaxation methods applied to determine the motion, in two dimensions, of a viscous fluid past a fixed cylinder, Quart. J. Mech. Appl. Math. 8 (1955), pp. 129–145. doi: 10.1093/qjmam/8.2.129
   Google Scholar
• L. Angermann and S. Wang, Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations, Appl. Numer. Math. 46 (2003), pp. 19–43. doi: 10.1016/S0168-9274(02)00224-6
   Web of Science ®Google Scholar
• G. Barles, Convergence of numerical schemes for degenerate parabolic equations arising in finance theory, in Numerical Methods in Finance, L.C.G. Rogers and D. Talay, eds., Cambridge University Press, Cambridge, 1997, pp. 1–21.
   Google Scholar
• D. Bertsimas, L. Kogan, and A.W. Lo, When is time continuous? J. Fin. Econ. 55 (2000), pp. 173–204. doi: 10.1016/S0304-405X(99)00049-5
   Web of Science ®Google Scholar
• F. Black, The pricing of commodity contracts, J. Fin. Econ. 3 (1976), pp. 167–179. doi: 10.1016/0304-405X(76)90024-6
   Web of Science ®Google Scholar
• Carbon Emissions Historical Data. http://www.investing.com/commodities/carbon-emissions-historical-data.
   Google Scholar
• R. Carmona, M. Fehr, and J. Hinz, Optimal stochastic control and carbon price formation, SIAM J. Control Optim. 48 (2009), pp. 2168–2190. doi: 10.1137/080736910
   Web of Science ®Google Scholar
• R. Carmona and J. Hinz, Risk-neutral models for emission allowance prices and option valuation, Manage. Sci. 57 (2011), pp. 1453–1468. doi: 10.1287/mnsc.1110.1358
   Web of Science ®Google Scholar
• S. Chang and J. Wang, Modeling CO2 emission prices and numerical valation of carbon derivatives under jump-diffusion process, Adv. Appl. Math. Mech. accepted.
   Google Scholar
• S. Chang, Z. Fang, X. Liu, and V. Shaydurov, A fitted finite volume method for unit-linked policy with surrender option, Comput. Res. 2 (2014), pp. 49–53.
   Google Scholar
• M. Chesney and L. Taschini, The endogenous price dynamics of the emission allowances and an application to CO2 option pricing, Appl. Math. Fin. 19 (2012), pp. 447–475. doi: 10.1080/1350486X.2011.639948
   Google Scholar
• J. Chevallier, Detecting instability in the volatility of carbon prices, Energy Econ. 33 (2011), pp. 99–110. doi: 10.1016/j.eneco.2010.09.006
   Web of Science ®Google Scholar
• M.G. Crandall, H. Ishii, and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, B. Am. Math. Soc. 27 (1992), pp. 1–68. doi: 10.1090/S0273-0979-1992-00266-5
   Web of Science ®Google Scholar
• G. Daskalakis, D. Psychoyios, and R.N. Markellos, Modeling CO2 emission allowance prices and derivatives: Evidence from the European trading scheme, J. Banking Fin. 33 (2009), pp. 1230–1241. doi: 10.1016/j.jbankfin.2009.01.001
   Web of Science ®Google Scholar
• R. Frey, Market illiquidity as a source of model risk in Dynamics, (2000). Available at http://sci-hub.org/downloads/4a92/[email protected]@239665933.pdf.
   Google Scholar
• P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer-Verlag, New York, NY, 2004.
   Google Scholar
• T. Hayashi and P.A. Mykland, Evaluating hedging errors: an asympotic approach, Math. Fin. 15 (2005), pp. 309–343. doi: 10.1111/j.0960-1627.2005.00221.x
   Web of Science ®Google Scholar
• J.E. Hilliard and J. Reis, Valuation of commodity futures and options under stochastic convenience yields, interest rates, and jump diffusions in the spot, J. Fin. Quant. Anal. 33 (1998), pp. 61–86. doi: 10.2307/2331378
   Web of Science ®Google Scholar
• J.C. Hull, The Greek letters, Options, Futures, and Other Derivatives, Reasson Education Limited, Edinburgh Gate, 2012, pp. 380–386.
   Google Scholar
• N. Koch, S. Fuss, G. Grosjean, and O. Edenhofer, Causes of the EU ETS price drop: Recession, CDM, renewable policies or a bit of everything? –New evidence, Energy Pol. 73 (2014), pp. 676–685. doi: 10.1016/j.enpol.2014.06.024
   Web of Science ®Google Scholar
• R.J. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, Cambridge, 2002.
   Google Scholar
• R.C. Merton, Option pricing when underlying stock returns are discontinuous, J. Fin. Econ. 3 (1976), pp. 125–144. doi: 10.1016/0304-405X(76)90022-2
   Web of Science ®Google Scholar
• D.D.S. Nel, Carbon Trading, Master Thesis, University of Oxford, 2009.
   Google Scholar
• M.S. Paolella and L. Taschini, An econometric analysis of emission allowance prices, J. Banking Fin. 32 (2008), pp. 2022–2032. doi: 10.1016/j.jbankfin.2007.09.024
   Web of Science ®Google Scholar
• J. Seifert, M. Uhrig-Homburg, and M. Wagner, Dynamic behavior of CO2 spot prices, J. Environ. Econ. Management 56 (2008), pp. 180–194. doi: 10.1016/j.jeem.2008.03.003
   Web of Science ®Google Scholar
• S.E. Shreve, Stochastic Calculus for Finance, Volume II: Continuous-Time Models, Springer-Verlag, New York, NY, 2004.
   Google Scholar
• R. Stanton, A nonparametric model of term structure dynamics and the market price of interest rate risk, J. Fin. 5 (1997), pp. 1973–2002. doi: 10.1111/j.1540-6261.1997.tb02748.x
   Google Scholar
• M. Tillmann, Valuation and Hedging of Carbon-Derivatives, Institut fu¨r Numerische und Angewandte Mathematik Fachbereich Mathematik, Münster, 2008.
   Google Scholar
• E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer-Verlag, New York, NY, 1999.
   Google Scholar
• S. Wang, A novel exponentially fitted triangular finite element method for an advection diffusion problem with boundary layers, J. Comput. Phys. 134 (1997), pp. 253–260. doi: 10.1006/jcph.1997.5691
   Web of Science ®Google Scholar
• S. Wang, A novel fitted finite volume method for the Black-Scholes equation govering option pricing, IMA J. Numer. Anal. 24 (2004), pp. 699–720. doi: 10.1093/imanum/24.4.699
   Web of Science ®Google Scholar
• S. Wang, S. Zhang, and Z. Fang, A superconvergent fitted finite volume method for Black-Scholes equations governing European and American option valuation, Numer. Methods PDEs 31 (2015), pp. 1190–1208. doi: 10.1002/num.21941
   Web of Science ®Google Scholar