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A Mixed Brownian-Poisson-fractional Model for option pricing
Liu Qian 1 #,Wang Xiaotian 2 *
1.Department of Mathematics,South China University of Technology, GuangZhou 501640
2.Department of Mathematics,South China University of Technology,501640
*Correspondence author
#Submitted by
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Funding: none
Opened online:23 November 2012
Accepted by: none
Citation: Liu Qian,Wang Xiaotian.A Mixed Brownian-Poisson-fractional Model for option pricing[OL]. [23 November 2012] http://en.paper.edu.cn/en_releasepaper/content/4496397
 
 
For option pricing, a mixed model with respect to standard Brownian motion and Poisson fractional process with 'Hurst exponent' being in (1/2,1) is established. We show that although return distributions of stocks are leptokurtic and skewed, have fatter tails than normal distribution and stock return series exhibit long-range dependence, the Black-Scholes formula still holds. We conclude that the skewed and fatter tail distributions as well as long-range dependence in stock return series are not fundamental factors to explain the smile effect of implied volatility in the Black-Scholes formula in some cases.
Keywords:Long-range dependence; Poisson fractional process; Option pricing
 
 
 

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