AI 中文总结
该研究扩展COS-TT-CHF方法，用TT-cross压缩特征函数张量，实现多资产期权快速定价，在高维场景下时间性能优于直接COS、张量傅里叶及QMC基准，可处理至d=30的GBM等场景。
AI 中文摘要
本文研究Lévy模型和仿射特征函数模型下的欧式多资产期权定价问题，主要障碍是维度灾难：直接的多维COS定价会形成张量积系数数组，其大小随资产数量呈指数增长。我们研究并扩展了COS-TT-CHF，这是一种低秩构造，它使用TT-cross将采样的特征函数张量压缩为张量-训练（tensor-train）COS系数，用于算术篮子期权以及最小/最大期权的定价。构建完成后，该压缩表示可快速完成设置后的行权价网格计算，以及选定分量的Delta/Vega计算。数值研究将其与自适应求积傅里叶基准、直接COS、张量傅里叶最小期权基准，以及基于随机Sobol点的拟蒙特卡洛（QMC）基准进行对比。报告的时间结果显示，当维度d从2变为4时，该方法相较于直接COS呈现出低维交叉优势；从d=3起，相较于张量傅里叶最小期权基准具有更优的时间性能；而在d=2时，相较于QMC通用Heston基准已具备更优的时间性能。所开展的测试在几何布朗运动（GBM）场景下达到d=30，在方差伽马（VG）、正态逆高斯（NIG）及通用Heston基准场景下达到d=20，期间全程报告了精度、秩、运行时间、控制敏感性，以及分量Delta/Vega的诊断结果。
英文摘要
This paper considers European multi-asset option pricing under Lévy and affine characteristic-function models. The main obstruction is the curse of dimensionality: direct multidimensional COS pricing forms tensor-product coefficient arrays whose size grows exponentially with the number of assets. We study and extend COS-TT-CHF, a low-rank construction that uses TT-cross to compress sampled characteristic-function tensors into tensor-train COS coefficients for arithmetic basket and min/max option pricing. Once built, the compressed representation gives fast post-setup strike-grid and selected component Delta/Vega calculations. The numerical study compares with adaptive-quadrature Fourier benchmarks, direct COS, a tensor-Fourier min-option benchmark, and quasi-Monte Carlo (QMC) references based on randomized Sobol points. The reported timings show a low-dimensional crossover against direct COS as the benchmark moves from $d=2$ to $d=4$, favorable timings against the tensor-Fourier min-option benchmark from $d=3$ onward, and favorable timings against the QMC common-Heston reference already at $d=2$. The reported tests reach $d=30$ for GBM and $d=20$ for VG, NIG, and common-Heston benchmark families, with accuracy, rank, runtime, control-sensitivity, and component Delta/Vega diagnostics reported throughout.
Comments35 pages, 3 figures, 17 tables
