• 论文 •

### 非线性Black-Scholes模型下障碍期权定

1. 贵州民族大学理学院, 贵阳 550025
• 出版日期:2016-04-25 发布日期:2016-05-09

SUN Yudong,WANG Xiufen,TONG Hong. BARRIER OPTIONS' PRICING UNDER THE NONLINEAR BLACK-SCHOLES MODEL[J]. Journal of Systems Science and Mathematical Sciences, 2016, 36(4): 513-527.

### BARRIER OPTIONS' PRICING UNDER THE NONLINEAR BLACK-SCHOLES MODEL

SUN Yudong ,WANG Xiufen ,TONG Hong

1. School of Science, Guizhou Minzu University, Guiyang 550025
• Online:2016-04-25 Published:2016-05-09

In this paper, the pricing problems of barrier options are discussed under the condition that the price of underlying asset follows the nonlinear Black-Scholes model. First, the parabolic initial- boundary value problems for barrier options are obtained by replicating strategy and Ito formula for the mixed fractional Brownian motion. Second, the author uses the perturbation method of single-parameter to obtain asymptomatic formulae of barrier options pricing problems. Finally, error estimates of these asymptotic solutions are illustrated by using the Feymann-Kac formula in which the results indicate that the asymptotic solutions uniformly converges to its exact solutions.

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