JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (04): 1-7.doi: 10.6040/j.issn.1671-9352.0.2014.160

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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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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

CLC Number: 

  • 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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