Efficiently pricing multi-asset options is a challenging problem in quantitative finance. When the characteristic function is available, Fourier-based methods are competitive compared to alternative techniques because the integrand in the frequency space often has a higher regularity than that in the physical space. However, when designing a numerical quadrature method for most Fourier pricing approaches, two key aspects affecting the numerical complexity should be carefully considered: (i) the choice of damping parameters that ensure integrability and control the regularity class of the integrand and (ii) the effective treatment of high dimensionality. We propose an efficient numerical method for pricing European multi-asset options based on two complementary ideas to address these challenges. First, we smooth the Fourier integrand via an optimized choice of the damping parameters based on a proposed optimization rule. Second, we employ sparsification and dimension-adaptivity techniques to accelerate the convergence of the quadrature in high dimensions. The extensive numerical study on basket and rainbow options under the multivariate geometric Brownian motion and some L\'evy models demonstrates the advantages of adaptivity and the damping rule on the numerical complexity of quadrature methods. Moreover, for the tested two-asset examples, the proposed approach outperforms the COS method in terms of computational time. Finally, we show significant speed-up compared to the Monte Carlo method for up to six dimensions.

翻译：高效定价多资产期权是量化金融中的一个具有挑战性的问题。当特征函数可用时，基于傅里叶的方法相比其他技术具有竞争力，因为频率空间中的被积函数通常比物理空间中的更光滑。然而，在设计大多数傅里叶定价方法的数值求积算法时，需要仔细考虑影响数值复杂度的两个关键方面：(i) 确保可积性并控制被积函数光滑性类别的阻尼参数选择，以及 (ii) 如何有效处理高维问题。我们提出了一种基于两个互补思想的数值方法，用于高效定价欧式多资产期权，以应对这些挑战。首先，通过基于所提出的优化规则最优选择阻尼参数，对傅里叶被积函数进行光滑化处理。其次，采用稀疏化和维度自适应技术加速高维求积的收敛。针对多元几何布朗运动及若干 Lévy 模型下的篮子期权与彩虹期权进行的广泛数值研究，展示了自适应性和阻尼规则对求积方法数值复杂度的优势。此外，在所测试的两资产示例中，所提出方法在计算时间上优于 COS 方法。最后，我们证明该方法在最多六维情形下相比蒙特卡洛方法实现了显著的加速效果。