次分数布朗运动下再装期权定价
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摘要
由于次分数Brown运动具有更一般的高斯过程特性,假设股票价格满足次分数Brown运动驱动的随机微分方程,在此基础上,应用次分数相关的随机分析理论,建立次分数下相应的金融数学模型,并借助保险精算方法对该模型进行求解,从而得到次分数Brown运动下的再装期权的定价公式.
The sub-fractional Brownian motion is a more general Gaussian process, so assuming that the stock price obeys the stochastic differential equation drove by sub-fractional Brownian motion and the financial market model in the sub-fractional Brownian motion environment is established. Using the sub-fractional Brownian stochastic analysis theory and the insurance actuarial method to get the pricing formula of the reload option under the sub-fractional Brownian motion is obtained.
The sub-fractional Brownian motion is a more general Gaussian process, so assuming that the stock price obeys the stochastic differential equation drove by sub-fractional Brownian motion and the financial market model in the sub-fractional Brownian motion environment is established. Using the sub-fractional Brownian stochastic analysis theory and the insurance actuarial method to get the pricing formula of the reload option under the sub-fractional Brownian motion is obtained.
引文
[1] 王献东, 杜雪樵.跳-扩散环境下的再装期权定价[J].经济数学,2007,24 (3): 276-282.
[2] JOHNSON S A, TIAN Y S. The value and incentive effects of nontraditional executive stock option plans[J]. Journal of Financial Economics,2000,57(1):3-34.
[3] 冯广波,刘再明,侯振挺.服从跳-扩散过程的再装期权股票期权的定价[J].系统工程学报,2003,18 (1):91-93.
[4] 罗春玲,王晓勤.股票价格服从分数布朗运动的再装期权定价[J].价值工程,2011 (13) :143-144.
[5] BOJDECKI T, GOROSTIZA L G, TALARCZYK A. Sub-fractional Brownian motion and its relation to occupation times[J]. Statistics and Probability Letters,2004,69 (4):405-419.
[6] YAN L T, HE K, CHEN C. The generalized Bouleau-Yor identity for a sub-fractional Brownian motion[J]. Seience China Mathematics,2013,56 (10) :2089-2116.
[7] 肖炜麟,张卫国,徐维军.次分数布朗运动下带交易费用的备兑权证定价[J].中国管理科学,2014,22 (5):1-7.
[8] 李萍,薛红,李琛伟.分数布朗运动下具有违约风险未定权益[J].纺织高校基础科学学报,2010,32 (2):109-112.
[9] 何永红,薛红,王晓东.分数布朗运动环境下再装期权的保险精算定价[J].纺织高校基础科学学报,2012,25(3):384-387.
[10] 傅强,喻建龙.再装期权定价及其在经理激励中的应用[J].商业研究,2006,11(1):147-150.
[11] 刘韶跃,杨向群.分数布朗运动环境中欧式未定权益的定价[J]. 应用概率统计,2004 (20) :429-434.
[2] JOHNSON S A, TIAN Y S. The value and incentive effects of nontraditional executive stock option plans[J]. Journal of Financial Economics,2000,57(1):3-34.
[3] 冯广波,刘再明,侯振挺.服从跳-扩散过程的再装期权股票期权的定价[J].系统工程学报,2003,18 (1):91-93.
[4] 罗春玲,王晓勤.股票价格服从分数布朗运动的再装期权定价[J].价值工程,2011 (13) :143-144.
[5] BOJDECKI T, GOROSTIZA L G, TALARCZYK A. Sub-fractional Brownian motion and its relation to occupation times[J]. Statistics and Probability Letters,2004,69 (4):405-419.
[6] YAN L T, HE K, CHEN C. The generalized Bouleau-Yor identity for a sub-fractional Brownian motion[J]. Seience China Mathematics,2013,56 (10) :2089-2116.
[7] 肖炜麟,张卫国,徐维军.次分数布朗运动下带交易费用的备兑权证定价[J].中国管理科学,2014,22 (5):1-7.
[8] 李萍,薛红,李琛伟.分数布朗运动下具有违约风险未定权益[J].纺织高校基础科学学报,2010,32 (2):109-112.
[9] 何永红,薛红,王晓东.分数布朗运动环境下再装期权的保险精算定价[J].纺织高校基础科学学报,2012,25(3):384-387.
[10] 傅强,喻建龙.再装期权定价及其在经理激励中的应用[J].商业研究,2006,11(1):147-150.
[11] 刘韶跃,杨向群.分数布朗运动环境中欧式未定权益的定价[J]. 应用概率统计,2004 (20) :429-434.