Abstract The PROJ method for pricing European options on one underlying asset was proposed by J. Lars Kirkby and then was applied to price Bermudan and Asian options. In this paper, we extend the method to higher dimensions, especially two-dimensions in which some exotic options can be priced. Our method does not rely on a-priori truncation of the integration range and exhibits excellent performance compared with other state-of-the-art methods, particularly for fatter-tailed short maturity models. We also discuss the errors introduced in each approximation and give corresponding error bounds. Numerical results on implementation of this method to price for popular two-assets options, under both the geometric Brownian Motion and Variance-Gamma dynamics, demonstrate remarkable accuracy and robustness.

中文翻译：

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通过框架对偶对两种标的资产的欧式期权进行有效定价

摘要 对一种标的资产的欧式期权定价的 PROJ 方法是由 J. Lars Kirkby 提出的，然后被应用于百慕大和亚洲期权的定价。在本文中，我们将该方法扩展到更高维度，尤其是可以定价一些奇异期权的二维。我们的方法不依赖于积分范围的先验截断，并且与其他最先进的方法相比表现出优异的性能，特别是对于肥尾短成熟度模型。我们还讨论了每个近似中引入的误差并给出了相应的误差界限。在几何布朗运动和方差-伽马动力学下，实施这种方法来为流行的双资产期权定价的数值结果显示出非凡的准确性和鲁棒性。