研究了原生资产价格遵循非线性Black-Scholes模型时障碍期权的定价问题. 首先,根据混合分数布朗运动的Ito公式和金融市场的复制策略,得到了障碍期权适合的抛物初边值问题. 其次,利用扰动理论中单参数摄动展开方法,给出了障碍期权的近似定价公式. 最后,利用Feyman-Kac公式分析了近似定价公式的误差估计问题,结果表明近似解一致收敛于相应期权价格的精确解.

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.