[1]黄凤云,刘国祥,王成冬,等.分数布朗运动情形下利率随机的双标的型两值期权定价[J].南京师大学报(自然科学版),2025,48(01):6-12.[doi:10.3969/j.issn.1001-4616.2025.01.002]
　Huang Fengyun,Liu Guoxiang,Wang Chengdong,et al.Pricing of Binary Options with Two Underlyings Under Stochastic Interest Rate About Fractional Brownian Motion[J].Journal of Nanjing Normal University(Natural Science Edition),2025,48(01):6-12.[doi:10.3969/j.issn.1001-4616.2025.01.002]
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分数布朗运动情形下利率随机的双标的型两值期权定价()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
48
期数:
2025年01期
页码:
6-12
栏目:
数学
出版日期:
2025-02-15

文章信息/Info

Title:
Pricing of Binary Options with Two Underlyings Under Stochastic Interest Rate About Fractional Brownian Motion
文章编号:
1001-4616(2025)01-0006-07
作者:
黄凤云1; 刘国祥2; 王成冬2; 章新婕2
(1.广西师范大学出版社,广西 桂林 541004)
(2.南京师范大学数学科学学院,江苏 南京 210023)
Author(s):
Huang Fengyun1; Liu Guoxiang2; Wang Chengdong2; Zhang Xinjie2
(1.Guangxi Normal University Press,Guilin 541004,China)
(2.School of Mathematical Sciences,Nanjing Normal University,Nanjing 210023,China)
关键词:
分数布朗运动; 随机利率; 拟鞅方法; 改变计价单位
Keywords:
fractional Brownian motion; random interest rate; quasi-martingale method; change valuation unit
分类号:
F830.9
DOI:
10.3969/j.issn.1001-4616.2025.01.002
文献标志码:
A
摘要:
主要利用不同计价单位的拟鞅方法,推导随机利率服从Vasicek模型,两种标的资产分别服从具有一定相关性的标准分数布朗运动的双标的型两值期权的定价公式.
Abstract:
In this paper,the quasi-martingale method with different pricing units is used to derive the pricing formulas of the two types of binary two-value options with the random interest rate obeying Vasicek model and the two types of underlying assets obeying the standard fractional Brownian motion with certain correlation.

参考文献/References:

[1]BACHELIER L. Theory of Speculation(translation of 1900 French edition),in Cootner[M]. The Random Character of Stock Market Price. Cambridge:MIT Press,1964:17-78.
[2]OSBORNE M F M. Brownian motion in the stock market[J]. Operations research,1959,7(2):145-173.
[3]BLACK F,SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of political economy,1973,81(3):637-654.
[4]MERTON R C. Theory of rational option pricing[J]. The bell journal of economics and management science,1973,4(1):141-183.
[5]EDGAR E P. A chaotic attractor for the S&p 500[J]. Financial analysts journal,1991,47(2):55-81.
[6]PETERS E E. Fractal market analysis:applying chaos theory to investment and economics[J]. Chaos theory,1994,34(2):343-345.
[7]LAURENT D,ALI S Ü. Fractional brownian motion:theory and applications[J]. ESAIM:proceedings,1998,5:75-86.
[8]DECREUSEFOND L,ÜSTÜNEL A S. Stochastic analysis of the fractional brownian motion[J]. Potential analysis,1999,10(2):177-214.
[9]HU Y Z,ΦKSENDAL B. Fractional white noise calculus and applications to finance[J]. Infinite dimensional analysis,quantum probability and related topics,2003,6(1):1-32.

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[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].南京师大学报(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.
[2]赵巍.股价受分数布朗运动驱动的混合期权定价模型[J].南京师大学报(自然科学版),2010,33(01):6.
　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.

备注/Memo

备注/Memo:
收稿日期:2024-05-16.
基金项目:国家社会科学基金项目(21BTJ044).
通讯作者:刘国祥,教授,研究方向:金融数学,金融统计. E-mail:gxliu63@163.com
更新日期/Last Update: 2025-02-15