随机利率下B-S模型基于非参数估计的期权保险精算定价
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摘要
引入服从Hull-White模型的随机利率,讨论了广义B-S模型欧式期权的保险精算定价问题.利用标的资产价格过程的实际概率测度和公平保费原理,得到了在期权有效期内有无红利支付两种情况下,欧式期权的保险精算定价公式.考虑到期权的保险定价问题依赖于未知的模型参数——标的资产价格的波动率、随机利率过程的漂移参数和波动率参数,利用资产价格和随机利率的观测数据,给出了基于模型参数估计的保险精算定价公式,并讨论了所得定价公式的相合性.
The actuarial pricing of European option for the general B-S models was studied by introducing the Hull-White stochastic interest rates. According to the physical probability measure of underlying assets and principle of fair premium,the actuarial pricings of European option were obtained under the conditions of paying dividends or without paying during the effective date of option. Considering the actuarial pricing depending on the unknown parameters,the volatility of underlying assets price,the drift parameters and diffusion parameter of the stochastic interest rates processes,the actuarial pricing formula based on the estimations of parameters were given by using the observed data of asses pricing and stochastic interest rates. The consistency of pricing formula was discussed.
The actuarial pricing of European option for the general B-S models was studied by introducing the Hull-White stochastic interest rates. According to the physical probability measure of underlying assets and principle of fair premium,the actuarial pricings of European option were obtained under the conditions of paying dividends or without paying during the effective date of option. Considering the actuarial pricing depending on the unknown parameters,the volatility of underlying assets price,the drift parameters and diffusion parameter of the stochastic interest rates processes,the actuarial pricing formula based on the estimations of parameters were given by using the observed data of asses pricing and stochastic interest rates. The consistency of pricing formula was discussed.
引文
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[11]闫海峰,刘三阳.股权价格遵循Ornstein-Uhlenback过程的期权定价[J].系统工程学报,2003,18(6):547-551.
[12]聂淑媛.基于X-12-ARIMA和AR-GARCH模型的房价波动研究[J].河南师范大学学报(自然科学版),2016,44(4):39-44.
[2]闫海峰,刘三阳.广义Black-Scholes模型期权定价新方法-保险精算方法[J].应用数学和力学,2003,24(7):730-738.
[3]王永茂,李丹,魏静.随机利率下基于Tsallis熵及O-U过程的幂式期权定价[J].郑州大学学报(理学版),2017,49(3):2-4.
[4]张东云.短期利率动态模型收益率和波动参数的估计[J].河南师范大学学报(自然科学版),2015,43(1):14-18.
[5]刘坚,文凤华,马超群.欧式期权和交换期权在随机利率及O-U过程下的精算定价方法[J].系统工程理论与实践,2009,29(12):118-124.
[6]陈松男.金融数学[M].上海:复旦大学出版社,2002:106-133.
[7]肖庆宪,郑祖康.股票价格过程方差函数的统计推断[J].应用概率统计,2000,16(2):182-190.
[8]KOO B,LINTON O.Semiparametric estimation of locally stationary diffusion models[J].Lse research online documents on economics,2010,170(1):439-477.
[9]KARATZAS I,SHREVE S.Brownian motion and stochastic calculus[M].New York:Springer,2000.
[10]吕海娟,彭江艳,武德安.变利率相依风险模型破产概率的积分方程和界[J].郑州大学学报(理学版),2016,48(1):39-44.
[11]闫海峰,刘三阳.股权价格遵循Ornstein-Uhlenback过程的期权定价[J].系统工程学报,2003,18(6):547-551.
[12]聂淑媛.基于X-12-ARIMA和AR-GARCH模型的房价波动研究[J].河南师范大学学报(自然科学版),2016,44(4):39-44.