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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.
This paper studies the pricing problem of barrier options when the native asset price follows the non-linear Black-Scholes model.Firstly, according to the Ito formula of mixed fractional Brownian motion and the replication strategy of financial markets, we get the initial parabolic initial value problem with barrier options.Secondly, By using perturbation theory, the approximate pricing formula of the barrier option is given.Finally, the error estimation of the approximate pricing formula is analyzed by the Feyman-Kac formula.The results show that the approximate solution converges uniformly to the exact price of the corresponding option solution.