在线阅读 --自然科学版 2020年2期《次分数布朗运动环境下后定选择权定价》
次分数布朗运动环境下后定选择权定价--[在线阅读]
王瑞, 薛红, 梁喜珠
西安工程大学 理学院, 陕西 西安 710048
起止页码: 105--113页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.02.003
摘要
为描述分数布朗运动难以描述的股价收益率变化非平稳的金融市场,假定股票价格服从次分数布朗运动,借助次分数随机分析理论和保险精算方法,得到了后定选择权定价公式.并通过分析期权价格灵敏度,说明各参数对期权价格有着不同的影响,另外给出了相应数值算例,表明金融市场不同的分形结构对期权价格有显著的影响.

Chooser Option Pricing in Sub-fractional Brownian Motion Environment
WANG Rui, XUE Hong, LIANG Xizhu
School of Science, Xi'an Polytechnic University, Shaanxi Xi'an 710048, China
Abstract:
In order to describe the non-stationary financial market in which the stock price returns change with fractional Brownian motion is difficult to describe,assume that the stock price obeys sub-fractional Brownian motion.The pricing formula of chooser option is obtained by the sub-fractional stochastic analysis theory and the insurance actuarial method.In addition,it shows each parameter has different influence on option price through the analysis of option price sensitivity,and numerical examples are given to show that different fractal structures of financial markets have significant effects on option prices.

收稿日期: 2019-08-06
基金项目: 国家自然科学基金(11601410);陕西省自然科学基础研究计划(2016JM1031);中国博士后科学基金(2017M613169)

参考文献:
[1]BLACK F,SCHOLES M.The Pricing of Options and Corporate Liabilities[J].Journal of Political Economy,1973,81(3):637-654.doi:10.1086/260062
[2]陈松男.金融工程学[M].上海:复旦大学出版社,2002:13-134. CHEN Songnan.Financial Engineering[M].Shanghai:Fudan University Press,2002:13-134.
[3]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(4):429-434.doi:10.3969/j.issn.1001-4268.2004.04.12 LIU Shaoyue,YANG Xiangqun.Pricing of European Claim in Fractional Brownian Motion Environment[J].Chinese Journal of Applied Probability,2004,20(4):429-434.
[4]BLADT M,RYDBERG H T.An Actuarial Approach to Option Pricing Under the Physical Measure and Without Market Assumptions[J].Insurance:Mathematics and Economics,1998,22(1):65-73.doi:10.1016/s0167-6687(98)00013-4
[5]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):730-739.doi:10.3321/j.issn.1000-0887.2003.07.010 YAN Haifeng,LIU Sanyang.New Method to Option Pricing for the General Black-Scholes Model:An Actuarial Approach[J].Applied Mathematics and Mechanics,2003,24(7):730-739.
[6]张元庆,蹇明.汇率连动期权的保险精算定价[J].经济数学, 2005,22(4):363-367.doi:10.3969/j.issn.1007-1660.2005.04.005 ZHANG Yuanqing,JIAN Ming.An Actuarial Approach to Quanto Option Pricing[J].Mathematics in Economics,2005,22(4):363-367.
[7]郑红,郭亚军,李勇,等.保险精算方法在期权定价模型中的应用[J].东北大学学报(自然科学版),2008,29(3):429-432.doi:10.3321/j.issn.1005-3026.2008.03.032 ZHENG Hong,GUO Yajun,LI Yong,et al.Application of Actuarial Approach to Option Pricing Model[J].Journal of Northeastern University(Natural Science),2008,29(3):429-432.
[8]王媛媛,薛红.分数Vasicek利率下创新重置期权定价[J].纺织高校基础科学学报,2015,28(1):62-71.doi:10.13338/j.issn:1006-8341.2015.01.015 WANG Yuanyuan,XUE Hong.Pricing Innovative Reset Options Under Ractional Vasicek Interest Rate[J].Basic Science Journal of Textile Universities,2015,28(1):62-71.
[9]毕学慧,杜雪樵.后定选择权的保险精算定价[J].合肥工业大学学报(自然科报),2007,30(5):649-651.doi:10.3969/j.issn.1003-5060.2007.05.032 BI Xuehui,DU Xueqiao.An Actuarial Approach to Chooser Option Pricing[J].Journal of Hefei University of Technology(Natural Science),2007,30(5):649-651.
[10]黄开元.分数布朗运动环境下后定选择权定价模型研究[D].西安:西安工程大学,2012:10-15. HUANG Kaiyuan.Chooser Option Pricing Model in Fractional Brownian Motion Environment[D].Xi'an:Xi'an Polytechnic University,2012:10-15.
[11]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.doi:10.1016/j.spl.2004.06.035
[12]TUDOR C.Some Properties of the Sub-fractional Brownian Motion[J].Stochastics,2007,79(5):431-448.doi:10.1080/17442500601100331
[13]YAN Litan,HE Kun,CHEN Chao.The Generalized Bouleauyor Identity for a Sub-fractional Brownian Motion[J].Seience China Mathematics,2013,56(10):2089-2116.doi:10.1007/s11425-013-4604-2
[14]程志勇,郭精军,张亚芳.次分数布朗运动下支付红利的欧式期权定价[J].应用概率统计,2018,34(1):37-48.doi:10.3969/j.issn.1001-4268.2018.01.004 CHENG Zhiyong,GUO Jingjun,ZHANG Yafang.Princing of European Option in Sub-factional Brownian Motion with Dividend Payments[J].Chinese Journal of Applied Probability and Statistics,2018,34(1):37-48.
[15]王佳宁,薛红.次分数布朗运动下再装期权定价[J].杭州师范大学学报(自然科学版),2019,18(2):180-184.doi:10.3969/j.issn.1674-232X.2019.02.012 WANG Jianing,XUE Hong.Reload Option Pricing in Sub-fractional Brownian Motion Environment[J].Journal of Hangzhou Normal University(Natural Science),2019,18(2):180-184.
[16]李丹,薛红.次分数布朗运动环境下可转换债券的定价[J].西安工程大学学报,2016,30(6):889-892.doi:10.13338/j.issn.1674-649X.2017.02.024 LI Dan,XUE Hong.Convertible Bond Pricing in Sub-fractional Brownian Motion Environment[J].Journal of Xi'an Polytechnic University,2016,30(6):889-892.
[17]申广君,何坤,闫理坦.次分数布朗运动的几点注记[J].山东大学学报(理学版),2011(3),46(3):102-108. SHEN Guangjun,HE Kun,YAN Litan.Remarks on Sub-fractional Brownian Motion[J].Journal of Shandong University(Natural Science),2011,46(3):102-108.
[18]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.doi:10.1638/j.cnki.issn1003-207X.2014.05.004 XIAO Weilin,ZHANG Weiguo,XU Weijun.Pricing Covered Warrants in a Sub-fractional Brownian Motion with Transaction Costs[J].Chinese Journal of Management Science,2014,22(5):1-7.
[19]李萍,薛红,李琛伟.分数布朗运动下具有违约风险未定权益定价[J].纺织高校基础科学学报,2012,25(4):462-466.doi:10.3969/j.issn.1006-8341.2012.04.015 LI Ping,XUE Hong,LI Chenwei.Credit-risky Claims Pricing in Fractional Brownian Motion Environment[J].Basic Sciences Journal of Textile Universities,2012,25(4):462-466.
[20]MOGENS B,RYDBERG T H.An Actuarial Approach to Option Pricing Under the Physical Measure and Without Market Assumptions[J].Insurance:Mathematics and Economics,1998,22(1):65-73.doi:10.1016/sd167-6687(98)00013-4
[21]薛红,王银利.双分数布朗运动模型下后定选择权定价[J].杭州师范大学学报(自然科学版),2017,16(3):301-306.doi:10.3969/j.issn.1674-232X.2017.03.014 XUE Hong,WANG Yinli.Chooser Option Pricing on Bi-fractional Brown Motion Model[J].Journal of Hangzhou Normal University(Natural Science),2017,16(3):301-306.