次分数布朗运动下带交易费用的备兑权证定价

中国管理科学 ›› 2014, Vol. 22 ›› Issue (5): 1-7.

• 论文 • 下一篇

次分数布朗运动下带交易费用的备兑权证定价

肖炜麟¹, 张卫国², 徐维军²

1. 浙江大学管理学院, 浙江杭州 310058;
2. 华南理工大学工商管理学院, 广东广州 510640

收稿日期:2012-03-14 修回日期:2013-11-06 出版日期:2014-05-20 发布日期:2014-05-14
作者简介:肖炜麟（1981-），男（汉族），湖南衡南人，浙江大学管理学院，副教授，研究方向：资产定价与数量金融.
基金资助:
国家社会科学基金重大招标项目（11&ZD156）；国家杰出青年科学基金资助项目（70825005）；国家自然基金资助项目（71101056，71171086）

Pricing Covered Warrants in a Sub-Fractional Brownian Motion with Transaction Costs

XIAO Wei-lin¹, ZHANG Wei-guo², XU Wei-jun²

1. School of Management, Zhejiang University, Hangzhou 310058, China;
2. School of Business Administration, South China University of Technology, Guangzhou 510640, China

Received:2012-03-14 Revised:2013-11-06 Online:2014-05-20 Published:2014-05-14

摘要/Abstract

摘要： 为了体现金融资产的长记忆性，采用次分数布朗运动刻画备兑权证标的资产价格变化的行为模式。利用随机分析理论和偏微分方程方法，建立了次分数布朗运动下带交易费用的备兑权证定价模型，进一步研究了定价模型的参数估计问题。最后，采用我国权证市场实际数据进行了实证分析，通过比较不同定价模型的结果说明了长记忆性和交易费用对定价结果有着显著的影响。

关键词: 次分数布朗, 交易费用, 备兑权证, 偏微分方程, 二次变差

Abstract: In order to reflect the long memory property of the financial asset, the sub-fractional Brownian motion is introduced to capture the underlying asset of covered warrants. The pricing model of covered warrants is proposed by using the theory of stochastic integration and the method of partial differential equations. Moreover, the problem of parameter estimation is also discussed in this paper. Finally, an empirical study based on China's warrant market is presented. The pricing results of different models illustrate that the long memory property and the transaction costs have a significant impact on pricing results.

Key words: sub-fractional Brownian motion, transaction costs, covered warrants, partial differential equation, quadratic variation

中图分类号:

F830.59

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.

XIAO Wei-lin, ZHANG Wei-guo, XU Wei-jun. Pricing Covered Warrants in a Sub-Fractional Brownian Motion with Transaction Costs[J]. Chinese Journal of Management Science, 2014, 22(5): 1-7.

参考文献

[1] Black F, Scholes M. The pricing of options and corporate liabilities [J]. Journal of Political Economy, 1973, 81(3): 637-657.

[2] Merton R C. Theory of rational option pricing [J]. The Bell Journal of Economics and Management Science, 1973, 4(1): 141-183.

[3] Leland H E. Option pricing and replication with transaction costs [J]. Journal of Finance, 1985, 40(5): 1283-1301.

[4] Damgaard A. Computation of reservation prices of options with proportional transaction costs [J]. Journal of Economic Dynamics and Control, 2006, 30(3):415-444.

[5] Tokarz K, Zastawniak T. American contingent claims under small proportional transaction costs [J]. Journal of Mathematical Economics, 2006, 43(1):65-85.

[6] Peters E E. Fractal structure in the capital markets [J]. Financial analyst Journal, 1989, 7(32): 434-453.

[7] 赵巍,何建敏.股票价格遵循分数Ornstein-Uhlenback过程的期权定价模型 [J].中国管理科学,2007,15 (3):1-5.

[8] 刘善存,宋殿宇,金华.分数布朗运动下带违约风险的可转换债券定价 [J].中国管理科学, 2011, 19(6): 25-30.

[9] Necula C. Option pricing in a fractional brownian motion environment [R]. Working paper of the Academy of Economic Studies, Bucharest (Romania), 2002.

[10] Xiao Weihin, Zhang Weiguo, Xu Weijun, et al. The valuation of equity warrants in a fractional Brownian environment [J]. Physica A, 2012, 391(4):1742-1752.

[11] 代军.权证定价中B-S模型与CSR 模型的比较[J].中国管理科学, 2009, 17(5): 20-26.

[12] 吴鑫育,周海林,马超群,等. 基于随机贴现因子方法的权证定价研究 [J].中国管理科学, 2012, 20(4): 1-7.

[13] Lin S J. Stochastic analysis of fractional Brownian motions [J]. Stochastics and Stochastics Reports, 1995, 55(1-2): 121-140.

[14] Duncan T E, Hu Yaozhong, Pasik-Duncan B. Stochastic calculus for fractional Brownian motion I. Theory [J]. SIAM Journal on Control and Optimization, 2000, 38(2): 582-612.

[15] Rogers L C G. Arbitrage with fractional Brownian motion [J]. Mathematical Finance,1997, 7(1):95-105.

[16] Bjrk T, Hult H. A note on Wick products and the fractional Black-Scholes model [J]. Finance and Stochastic, 2005, 9(2):197-209.

[17] Tudor C. Some properties of the sub-fractional Brownian motion [J]. Stochastics, 2007, 79(5):431-448.

[18] Tudor C. Inner product spaces of integrands associated to sub-fractional Brownian motion [J]. Statistics and Probability Letters, 2008, 78(14):2201-2209.

[19] Tudor C. Sub-fractional Brownian motion as a model in finance. Working Paper,Ann. Univ. Bucuresti, Mathematica, 2008.

[20] Yan Litan, Shen Gangjun, He Kun. It's formula for the sub-fractional Brownian motion [J]. Communication on Stochastic Analysis, 2011, 5(1):135-159.

[21] Nualart D, Taqqu M S. Wick-It formula for regular processes and applications to the Black and Scholes formula [J]. Stochastics: An International Journal of Probability and Stochastic Processes, 2008, 80(5): 477-487.

[22] Hull J C. Options, futures, and other derivatives [M].5th ed.New Jersey: Prentice Hall College Div, 5th edition, 2002.

次分数布朗运动下带交易费用的备兑权证定价

Pricing Covered Warrants in a Sub-Fractional Brownian Motion with Transaction Costs

PDF (PC)

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

Metrics

本文评价

推荐阅读 10

[1]	苑慧玲, 徐路, 周勇. 带有市场交易信息和随机微观噪声下的杠杆效应研究[J]. 中国管理科学, 2020, 28(9): 12-22.
[2]	孙卫, 尚磊, 梁矶华. 基于削减量与交易费用的垄断厂商治污技术投资决策模型研究[J]. 中国管理科学, 2010, 18(3): 33-37.
[3]	李志生. 最优交易策略问题的动态求解方法[J]. 中国管理科学, 2008, 16(3): 102-108.
[4]	姚玲珍, 杨大楷. 中国对外直接投资方式的选择[J]. 中国管理科学, 2003, (2): 11-15.