In this paper, the valuation of the discrete barrier options on the condition that the underlying asset price process follows the GARCH volatility and double exponential jump is studied. We derived an analytical approximation of the characteristic function for the underlying log-asset price. Then, a quasianalytical approximate formula of the price of the discrete barrier option is obtained based the on Fourier-cosine method. Numerical examples show that the Fourier-cosine method is fast and efficient for pricing discrete barrier options compared with the Monte Carlo simulation method. Finally, the influences of some important parameters on the prices of discrete barrier options are studied to further illustrate the rationality of the model.

中文翻译：

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随机波动率和双指数跳变条件下离散监测的壁垒期权定价的傅里叶-余弦方法

本文研究了在基础资产价格过程遵循GARCH波动率和双指数跳跃的条件下离散障碍期权的估值。我们得出了基本对数资产价格的特征函数的解析近似值。然后，基于傅立叶-余弦法，获得了离散障碍期权价格的拟解析近似公式。数值算例表明，与蒙特卡罗模拟方法相比，傅立叶余弦法可快速有效地为离散障碍物定价。最后，研究了一些重要参数对离散障碍期权价格的影响，以进一步说明该模型的合理性。