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 optimized choice of 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, the approach achieves substantial computational gains compared to the Monte Carlo method.

翻译：多资产期权的高效定价是量化金融中的一个挑战性问题。当特征函数可用时，基于傅里叶的方法与其他技术相比具有竞争优势，因为频率空间中的被积函数往往比物理空间中的被积函数具有更高的正则性。然而，在设计大多数傅里叶定价方法的数值求积方案时，需谨慎考虑影响数值复杂性的两个关键方面：（i）阻尼参数的选择，其确保可积性并控制被积函数的正则性类别；（ii）高维度的有效处理。我们提出了一种基于两个互补思路的高效数值方法，用于对欧式多资产期权进行定价，以应对这些挑战。首先，我们通过基于所提出的优化规则选择阻尼参数来平滑傅里叶被积函数。其次，我们采用稀疏化与维度自适应技术来加速高维求积的收敛性。在多元几何布朗运动及某些Lévy模型下对篮子期权和彩虹期权进行的大量数值研究，展示了自适应性与阻尼规则对求积方法数值复杂性的优势。此外，与蒙特卡洛方法相比，该方法实现了显著的计算增益。