STN-GPR：一种用于高效期权定价的奇异张量网络框架
STN-GPR: A Singularity Tensor Network Framework for Efficient Option Pricing
AI总结：
本文提出STN-GPR框架，利用张量网络近似方法高效解决大规模投资组合重估问题，通过TT形式表示高维价格表面，实现无需完整训练张量的近似，并在噪声无设置下进行TT基于高斯过程回归。
摘要：
我们开发了一种张量网络替代方案用于期权定价，旨在解决市场风险管理中出现的大规模投资组合重估问题（例如VaR和预期短缺计算）。该方法涉及使用TT交叉近似将高维价格表面表示为张量列车（TT）形式，并直接从黑箱价格评估构建替代方案，而无需生成完整的训练张量。对于推理，我们使用拉普拉斯核并推导出核矩阵及其闭式反演的TT表示形式，在无噪声设置下实现基于TT的高斯过程回归，而无需密集矩阵分解或迭代线性求解。我们发现超参数优化一致倾向于较大的核长度尺度，并证明在该情况下GPR预测器在离格输入时减少为多线性插值；我们还推导出该极限的低秩TT表示形式。我们在五个资产篮子期权上评估了该方法，覆盖了八维参数空间（资产现货水平、行权价、利率和到期时间）。对于欧洲几何篮子看跌期权，张量替代方案在较短的训练时间内实现了比标准GPR更低的测试误差。对于训练于LSMC数据的美国算术篮子看跌期权，替代方案在训练集规模上表现出更有利的扩展性，同时提供毫秒级的每个查询评估时间，总体运行时间主要由数据生成决定。
英文摘要：
We develop a tensor-network surrogate for option pricing, targeting large-scale portfolio revaluation problems arising in market risk management (e.g., VaR and Expected Shortfall computations). The method involves representing high-dimensional price surfaces in tensor-train (TT) form using TT-cross approximation, constructing the surrogate directly from black-box price evaluations without materializing the full training tensor. For inference, we use a Laplacian kernel and derive TT representations of the kernel matrix and its closed-form inverse in the noise-free setting, enabling TT-based Gaussian process regression without dense matrix factorization or iterative linear solves. We found that hyperparameter optimization consistently favors a large kernel length-scale and show that in this regime the GPR predictor reduces to multilinear interpolation for off-grid inputs; we also derive a low-rank TT representation for this limit. We evaluate the approach on five-asset basket options over an eight dimensional parameter space (asset spot levels, strike, interest rate, and time to maturity). For European geometric basket puts, the tensor surrogate achieves lower test error at shorter training times than standard GPR by scaling to substantially larger effective training sets. For American arithmetic basket puts trained on LSMC data, the surrogate exhibits more favorable scaling with training-set size while providing millisecond-level evaluation per query, with overall runtime dominated by data generation.
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