基于机制转换模型的碳排放权期权定价
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摘要
机制转换模型可以将外部环境的变化迅速反映到对模型参数的调整中,故运用马氏链刻画外部机制建立机制转换模型,基于此进行碳排放权期权定价。为实现其价值函数的数值计算,首次设计并证明了一套倒向递归算法,该算法依据马氏链跳跃的划分实现递归,从而克服了马氏链带来的运算高复杂度,其数值结果展示了完整的波动率微笑和期限结构。最后通过与前人提出的算法以及蒙特卡洛模拟比较表明,倒向递归算法可获得更高的准确性和运算效率。
Regime switching reflects the changes of external environment of market into the adjustment of the model parameters, hence Markov chains are applied to capture the external regime in order to establish the regimes witching model, based on which the carbon emission allowance is priced. For the purpose of numerical implement of value functions, a backward recursive algorithm is designed and theoretically proved. The recursion relies on the division of whether the Markov chain jumps, and it conquers the high computational complexity brought by the Markov chain. Numerical results obtained by this approach present a completed volatility smile and term structure. Finally through the comparison with former algorithm and Monte Carlo simulation, this algorithm outperforms them in terms of precision and computational efficiency.
Regime switching reflects the changes of external environment of market into the adjustment of the model parameters, hence Markov chains are applied to capture the external regime in order to establish the regimes witching model, based on which the carbon emission allowance is priced. For the purpose of numerical implement of value functions, a backward recursive algorithm is designed and theoretically proved. The recursion relies on the division of whether the Markov chain jumps, and it conquers the high computational complexity brought by the Markov chain. Numerical results obtained by this approach present a completed volatility smile and term structure. Finally through the comparison with former algorithm and Monte Carlo simulation, this algorithm outperforms them in terms of precision and computational efficiency.
引文
[1] Jensen J, Rasmussen T N. Allocation of CO_2 emissions permits:A general equilibrium analysis of policy instruments[J]. Journal of environmental economies and management, 2000, 40(2):111-136.
[2]冯路,王天庆·中国碳排放权初始分配定价研究[J].学习与实践,2014,(4):45-51.
[3]金永利,李晓清,楚京京.我国碳排放权的交易问题及对策分析[J].商业会计,2015,(18):85-87.
[4]吴恒煜,胡根华.国际碳排放权市场动态相依性分析及风险测度:基于Copula-LARCH模型[J].数理统计与管理,2014, 33(5):892-909.
[5]吴振信,万埠磊,王书平,胡爱梅.欧盟碳价波动的结构突变特性检验[J].数理统计与管理:2015, 34(6):969-977.
[6] Benz E, Truck S. Modeling the price dynamics of CO_2 emission allowances[J]. Energy economics,2009, 31(1):4-15.
[7]王锐.碳排放权交易的市场定价[D].哈尔滨工业大学,硕士论文,2010.
[8]张建清,周丽丽,郭荣鑫.我国碳排放权定价方式选择一基于Black-Scholes模型检验[J].广东外语外贸大学学报,2012,(5):51-55.
[9]赵小攀,李朝红,任晓鸽.基于Black-Scholes期权定价模型的碳排放权定价[J].财务管理与资本运营,2016,(7):28-31.
[10]吴恒煜,胡根华,秦嗣毅.次贷危机下中国股市与国外股市相依性分析一基于Markov机制转换模型[J].数理统计与管理,2013, 32(2):343-358.
[11] Yang A J, Liu Y, Xiang J, Yang H Q. Optimal buying at the global minimum in a regime switching model[J]. Mathematical Social Sciences, 2016, 84:50-55.
[12] Hardy M R. A regime-switching model of long-term stock returns[J]. North American Actuarial Journal, 2002, 6(1):171-173.
[13] Hull J C. Options, Futures, and Other Derivatives(9thEd)[M]. Prentice Hall, 2014.
[14] Yao D D, Zhang Q, Zhou X Y. A regime-switching model for European options[J]. International series in operation research and management science, 2006,(94):281-300.
[15] Oksendal B. Stochastic Differential Equations(5th edition)[M]. Springer-Verlag, 2000.
[16] Privault N. Understanding Markov Chains—Examples and Applications[M]. Springer, 2013.
[2]冯路,王天庆·中国碳排放权初始分配定价研究[J].学习与实践,2014,(4):45-51.
[3]金永利,李晓清,楚京京.我国碳排放权的交易问题及对策分析[J].商业会计,2015,(18):85-87.
[4]吴恒煜,胡根华.国际碳排放权市场动态相依性分析及风险测度:基于Copula-LARCH模型[J].数理统计与管理,2014, 33(5):892-909.
[5]吴振信,万埠磊,王书平,胡爱梅.欧盟碳价波动的结构突变特性检验[J].数理统计与管理:2015, 34(6):969-977.
[6] Benz E, Truck S. Modeling the price dynamics of CO_2 emission allowances[J]. Energy economics,2009, 31(1):4-15.
[7]王锐.碳排放权交易的市场定价[D].哈尔滨工业大学,硕士论文,2010.
[8]张建清,周丽丽,郭荣鑫.我国碳排放权定价方式选择一基于Black-Scholes模型检验[J].广东外语外贸大学学报,2012,(5):51-55.
[9]赵小攀,李朝红,任晓鸽.基于Black-Scholes期权定价模型的碳排放权定价[J].财务管理与资本运营,2016,(7):28-31.
[10]吴恒煜,胡根华,秦嗣毅.次贷危机下中国股市与国外股市相依性分析一基于Markov机制转换模型[J].数理统计与管理,2013, 32(2):343-358.
[11] Yang A J, Liu Y, Xiang J, Yang H Q. Optimal buying at the global minimum in a regime switching model[J]. Mathematical Social Sciences, 2016, 84:50-55.
[12] Hardy M R. A regime-switching model of long-term stock returns[J]. North American Actuarial Journal, 2002, 6(1):171-173.
[13] Hull J C. Options, Futures, and Other Derivatives(9thEd)[M]. Prentice Hall, 2014.
[14] Yao D D, Zhang Q, Zhou X Y. A regime-switching model for European options[J]. International series in operation research and management science, 2006,(94):281-300.
[15] Oksendal B. Stochastic Differential Equations(5th edition)[M]. Springer-Verlag, 2000.
[16] Privault N. Understanding Markov Chains—Examples and Applications[M]. Springer, 2013.
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