非线性Black-Scholes模型下障碍期权定

BARRIER OPTIONS' PRICING UNDER THE NONLINEAR BLACK-SCHOLES MODEL

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 initialboundary 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.