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山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (04): 1-7.doi: 10.6040/j.issn.1671-9352.0.2014.160

• 论文 •    下一篇

基于Tsalli熵分布及O-U过程的幂式期权定价

赵攀1,2, 肖庆宪1   

  1. 1. 上海理工大学管理学院, 上海 200093;
    2. 皖西学院金融与数学学院, 安徽 六安 237012
  • 收稿日期:2014-04-14 修回日期:2014-12-22 出版日期:2015-04-20 发布日期:2015-04-17
  • 作者简介:赵攀(1980-),男,博士研究生,研究方向为金融工程、金融数学.E-mail:zhaopan@wxc.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11171221);上海市一流学科基金项目(XTKX2012);安徽省高校优秀青年基金项目(2012SQRL196)

Pricing of power options based on Tsallis distribution and O-U process

ZHAO Pan1,2, XIAO Qing-xian1   

  1. 1. Business School, University of Shanghai for Science and Technology, Shanghai 200093, China;
    2. College of Finance and Mathematics, West Anhui University, Lu'an 237012, Anhui, China
  • Received:2014-04-14 Revised:2014-12-22 Online:2015-04-20 Published:2015-04-17

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摘要： 考虑资产收益率分布的尖峰厚尾、长期相依和资产价格的均值回复性,选取具有尖峰厚尾和长期相依特征的Tsallis熵分布及均值回复性的O-U过程建立资产价格的运动模型,运用随机微分和等价测度鞅方法研究了幂型欧式期权的定价问题,得到了资产价格遵循最大化Tsallis熵分布的幂型欧式看涨及看跌期权的定价公式,该公式推广了经典的Black-Scholes公式,拓展了已有文献的结论.

关键词: Tsallis熵, O-U过程, 幂式期权, 鞅

Abstract: Characteristics of fat-tail, long-term dependence of return distribution and mean reversion of asset prices were considered. Thus, the distribution of Tsallis entropy, which has fat-tailed and long-term dependent characteristics, and O-U process were selected to describe the law of the asset prices movement. By using the stochastic differential and martingale, the pricing of power European options was studied. The pricing formulas of power European call and put options, under the asset prices following the maximum Tsallis entropy distribution, were obtained, and the formulas not only generalize the classical Black-Scholes' conclusion, but also contain the conclusions in the other literatures.

Key words: O-U process, power options, martingale, Tsallis entropy

中图分类号: 

  • F830.9
[1] BLACK F, SCHOLES M. The pricing of options and corporate liabilities[J]. Journal of Political Economy, 1973, 81:133-155.
[2] MANDELBROT B. The variation of certain speculative pricings[J]. Journal of Business, 1963, 36:394-419.
[3] FAMA E F. The behavior of stock market prices[J]. Journal of Business, 1965, 38: 34-105.
[4] BLATTBERG R, GONEDES N. A comparison of stable and student distributions as statistical models for stock prices[J]. Journal of Business, 1974, 47:244-280.
[5] CONT R. Empirical properties of asset returns: stylized facts and statistical issues[J]. Quantitative Finance, 2001, 1:223-236.
[6] LO A. Long term memory in stock market prices[J]. Econometrica, 1991, 59:1279-1313.
[7] LUX T. The stable Paretian hypothesis and the frequency of large returns: an examination of major German stocks[J]. Applied Financial Economics, 1996, 6:463-485.
[8] DING Zhuanxin, GRANGER C W J, ENGLE R F. A long memory property of stock market returns and a new model[J]. Journal of Empirical Finance, 1993, 1(1):83-106.
[9] 闫海峰, 刘三阳. 股票价格遵循Ornstein-Uhlenback过程的期权定价[J]. 系统工程学报, 2003, 20(11):429-434. YAN Haifeng, LIU Sanyang. Pricing options on stocks driven by Ornstein-Uhlenback process[J]. Journal of Systems Engineering, 2003, 20(11):429-434.
[10] 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. ZHAO Wei, HE Jianmin. Model of option pricing driven by fractional Ornstein-Uhlenback process[J]. Chinese Journal of Management Science, 2007, 15(3):1-5.
[11] 刘坚, 文凤华, 马超群. 欧式期权和交换期权在随机利率及O-U过程下的精算定价方法[J]. 系统工程理论与实践, 2009, 29(12):118-124. LIU Jian, WEN Fenghua, MA Chaoqun. Actuarial pricing approach to Europe option and exchange option under stochastic interest rates and O-U process[J]. Systems Engineering: Theory & Practice, 2009, 29(12):118-124.
[12] KOZUKI N, FUCHIKAMI N. Dynamical model of financial markets: fluctuating‘temperature’causes intermittent behavior of price changes[J]. Physica A, 2003, 329(1-2):222-230.
[13] RYUJI I, MASAYOSHI I. Time-series analysis of foreign exchange rates using time-dependent pattern entropy[J]. Physica A, 2013, 392:3344-3350.
[14] MICHAEL F, JOHNSON M D. Financial market dynamics[J]. Physica A, 2003, 32:525-534.
[15] OREN J TAPIERO. A maximum (non-extensive) entropy approach to equity options bid-ask spread[J]. Physica A, 2013, 292:3051-3060.
[16] BORLAND L. A Theory of Non-Gaussian Option pricing[J]. Quantitative Finance, 2002, 2:415-431.
[17] YURI A, KATZ, LI Tian. q-Gaussian distributions of leverage returns, first stopping times, and default risk valuations[J]. Physica A, 2013, 292:4989-4996.
[18] ADRIANA P, FERNANDO M, REINALDO R, et al. Value-at-risk and Tsallis statistics: risk analysis of the aerospace sector[J]. Physica A, 2004, 344:554-561.
[19] PLASTINO A R, PLASTINO A. Non-extensive statistical mechanics and generalized Fokker-Planck equation[J]. Physica A, 1995, 222:347-354.
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