In this paper, we study a new type of barrier option, which is called ‘double volatility barriers option’. Take the European up-and-out option as an example, the option will become worthless if the volatility of underlying asset becomes too high and reaches or exceeds the barrier. One advantage of this kind of option is to help option holders effectively control volatility risk. To price double volatility barriers option, we use the eigenfunction expansion method to approximate the solution to the partial differential equation that the option price satisfies. We also obtain the estimation formulae for model parameters by the martingale method and the numerical simulations of the option price are provided for the demonstration purpose.

在本文中，我们研究了一种新型的壁垒期权，称为“双重波动壁垒期权”。以欧洲上落式期权为例，如果基础资产的波动性过高并达到或超过障碍，则该期权将变得一文不值。这种期权的优点之一是可以帮助期权持有人有效地控制波动风险。为了对双波动障碍期权定价，我们使用特征函数展开法对期权价格满足的偏微分方程进行近似求解。我们还通过the方法获得了模型参数的估计公式，并提供了期权价格的数值模拟，以供演示之用。