×

Singular forward-backward stochastic differential equations and emissions derivatives. (English) Zbl 1276.60070

The authors are interested in modelling \(CO_{2}\) emissions, and in particular the valuation \(CO_{2}\) emission allowances. For this they propose two forward-backward stochastic differential equations with singular terminal condition as models. They also provide a first order Taylor expansion and show how to numerically calibrate some of their models to be used in \(CO_{2}\) option pricing.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
91G80 Financial applications of other theories
91G20 Derivative securities (option pricing, hedging, etc.)
PDF BibTeX XML Cite
Full Text: DOI arXiv Euclid

References:

[1] Barles, G. and Souganidis, P. E. (1991). Convergence of approximation schemes for fully nonlinear second order equations. Asymptot. Anal. 4 271-283. · Zbl 0729.65077
[2] Belaouar, R., Fahim, A. and Touzi, N. (2010). Optimal production policy under carbon emission market.
[3] Carmona, R., Fehr, M. and Hinz, J. (2009). Optimal stochastic control and carbon price formation. SIAM J. Control Optim. 48 2168-2190. · Zbl 1203.93209
[4] Carmona, R., Fehr, M., Hinz, J. and Porchet, A. (2010). Market design for emission trading schemes. SIAM Rev. 52 403-452. · Zbl 1198.91166
[5] Carmona, R. and Hinz, J. (2011). Risk neutral modeling of emission allowance prices and option valuation. Management Science 57 1453-1468. · Zbl 1279.91202
[6] Chesney, M. and Taschini, L. (2008). The endogenous price dynamics of the emission allowances: An application to CO2 option pricing. Technical report. · Zbl 1372.91079
[7] Delarue, F. (2002). On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case. Stochastic Process. Appl. 99 209-286. · Zbl 1058.60042
[8] Delarue, F. and Guatteri, G. (2006). Weak existence and uniqueness for forward-backward SDEs. Stochastic Process. Appl. 116 1712-1742. · Zbl 1113.60059
[9] Krylov, N. V. (1996). Lectures on Elliptic and Parabolic Equations in Hölder Spaces. Graduate Studies in Mathematics 12 . Amer. Math. Soc., Providence, RI. · Zbl 0865.35001
[10] Kunita, H. (1990). Stochastic Flows and Stochastic Differential Equations. Cambridge Studies in Advanced Mathematics 24 . Cambridge Univ. Press, Cambridge. · Zbl 0743.60052
[11] Lax, P. D. (2006). Hyperbolic Partial Differential Equations. Courant Lecture Notes in Mathematics 14 . New York Univ., New York. · Zbl 1113.35002
[12] Ma, J., Wu, Z., Zhang, D. and Zhang, J. (2010). On wellposedness of forward-backward SDEs-a unified approach.
[13] Ma, J. and Yong, J. (1999). Forward-Backward Stochastic Differential Equations and Their Applications. Lecture Notes in Math. 1702 . Springer, Berlin. · Zbl 0927.60004
[14] Nualart, D. (1995). The Malliavin Calculus and Related Topics . Springer, New York. · Zbl 0837.60050
[15] Pardoux, É. and Peng, S. (1992). Backward stochastic differential equations and quasilinear parabolic partial differential equations. In Stochastic Partial Differential Equations and Their Applications ( Charlotte , NC , 1991). Lecture Notes in Control and Information Sciences 176 200-217. Springer, Berlin. · Zbl 0766.60079
[16] Peng, S. and Wu, Z. (1999). Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 825-843. · Zbl 0931.60048
[17] Pham, H. (2009). Continuous-Time Stochastic Control and Optimization with Financial Applications. Stochastic Modelling and Applied Probability 61 . Springer, Berlin. · Zbl 1165.93039
[18] Rogers, L. C. G. and Williams, D. (1994). Diffusions , Markov Processes , and Martingales. Vol. 2, 2nd ed. Cambridge Univ. Press, Cambridge. · Zbl 0977.60005
[19] Seifert, J., Uhrig-Homburg, M. and Wagner, M. (2008). Dynamic behavior of carbon spot prices. Theory and empirical evidence. Journal of Environmental Economics and Management 56 180-194. · Zbl 1146.91355
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.