[1]赵巍.股价受分数布朗运动驱动的混合期权定价模型[J].南京师范大学学报(自然科学版),2010,33(01):6-10.
 Zhao Wei.Pricing of Compound Option Model With Stock Price Driven by FBM[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(01):6-10.
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股价受分数布朗运动驱动的混合期权定价模型()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年01期
页码:
6-10
栏目:
数学
出版日期:
2010-03-20

文章信息/Info

Title:
Pricing of Compound Option Model With Stock Price Driven by FBM
作者:
赵巍;
淮海工学院商学院
Author(s):
Zhao Wei
School of Business,Huaihai Institute of Technology,Lianyungang 222001,China
关键词:
分数布朗运动 拟鞅定价 分数B lack-Scho les模型 混合期权
Keywords:
fractiona l brown ian m otion quas-im arting ale pricing fractiona l B lack-Scho les model compound option
分类号:
F830.91;F224
摘要:
分数布朗运动由于具有自相似和长期相关等分形特性,已成为数理金融研究中更为合适的工具.本文通过假定股票价格服从几何分数布朗运动,构建了It分数Black-Scholes市场;接着在分数风险中性测度下,利用随机微分方程和拟鞅(quasi-martingale)定价方法给出了分数Black-Scholes定价模型;进而讨论了股价受分数布朗运动驱动的混合期权定价模型.研究结果表明,与标准期权价格相比,分数期权价格要同时取决于到期日和Hurst参数.
Abstract:
The se l-f sim ilar ity and long- rang e dependence properties m ake the Frac tiona l B rown ian m otion a suitable too l in d ifferen t applications likem a them atical finance. Th is paper used the hypotheses that asse rt price follow ed geome tr ic FBM to construct the It? fractional B lack-Scholes m arket. U sing of quas-i m artinga lem ethod based on the fractiona l r isk neutra lm easure, this paper so lved fractiona l Black-Scho les m ode.l M oreove r pr ic ing of com pound option mode l w ith stock pr ice dr iven by FBM w as discussed. The result show ed frac tiona l option pr ice, compared to c lassical option price, depends on m atur ity tim e and H urst parameter.

参考文献/References:

[ 1]Bache lier L. Theory o f Specu la tion[M ] / / Coo tner P. The Random Character o f Stock M arket Pr ices. C ambr idge: M IT Press, 1900: 17-78.
[ 2]Sumue lson P A. Rational theo ry o f wa rrants pr ic ing [ J]. IndustrialM agem ent Rev iew, 1965, 6( 1): 13-31.
[ 3]O sborneM FM. B rown ian m otion in the stock m arket[ J]. Operations Research, 1959, 7( 2): 145-173.
[ 4]M ande lbrot B B, Van Ness JW. Fractional Brown ian mo tion, fractiona l no ises and application[ J]. SIAM Rev iew, 1968, 10 ( 4): 422-437.
[ 5]L in S J. Stochastic ana lysis of frac tiona l Brow nian m otion[ J]. S to chastics and Stochastics Reports, 1995, 55( 1): 121-140.
[ 6]Roger L C G. Arbitrage w ith fractiona l Brow nian mo tion[ J] . M a them atical F inance, 1997, 7( 11): 95-105.
[ 7]Decreusefond L, Ustunel A S. Stochastic analysis o f the fractiona l Brown ian mo tion[ J] . Potential Ana ly sis, 1999, 10( 2): 177-214.
[ 8]H u Yaozhong, ? ksendal B. Fractiona l wh ite no ise ca lculus and application to finance [ J] . In finite D imensional Ana lys is, Quantum Probab ility and Re lated Topics, 2003, 6( 1): 1-32.
[ 9]Necu la C. Option pr ic ing in a fractional Brownian m o tion env ironm en t[ EB /OL] . [ 2008-03-10 ]. http: / /www. dofin. ase. ro /.
[ 10]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( 11) : 429-434.
[ 11]陈松男. 金融工程学[M ]. 上海: 复旦大学出版社, 2002.

相似文献/References:

[1]赵巍.分数布朗运动环境下降低权利金的权证定价研究[J].南京师范大学学报(自然科学版),2012,35(03):11.
 Zhao Wei.Research on Pricing of Depressed Option Stock Under Fractional Brownian Motion Environment[J].Journal of Nanjing Normal University(Natural Science Edition),2012,35(01):11.

备注/Memo

备注/Memo:
基金项目: 淮海工学院引进人才科研启动基金( KQ09012) .
通讯联系人: 赵 巍, 博士, 讲师, 研究方向: 金融复杂性和金融工程. E-mail:njzhaow@126.com
更新日期/Last Update: 2013-04-08