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
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