发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对不完全市场期权定价问题，提出学习拉东-尼科迪姆导数的神经网络XiNet，其在路径依赖权益定价上优于基准方法，可一致定价各类权益。
AI 中文摘要
在不完全市场中，无套利（NFLVR）确保存在等价局部鞅测度（ELMM），但该测度不唯一：无法对冲的风险（跳跃、随机波动率）对应一整族等价测度，仅资产动态无法确定市场选择的那一个测度。我们刻画了期权数据下Q的可识别性，提出一种可从数据识别且能一致定价任何权益的测度。关键边界是“识别墙”：欧式期权仅能识别终端边际分布，而样本外尾部、路径/联合结构需要与定价风险匹配的工具（方差或更高矩互换、路径依赖权益）。在此视角下，最小相对熵加权蒙特卡洛（WMC）是边际分布的最优基准；我们将其推广为由物理场景上的神经网络参数化的全路径空间测度变换——XiNet，该模型直接从8个无模型路径特征学习ξ=dℚ/dℙ，以期权价格为软约束。在欧式（边际）定价任务中，XiNet的表现与WMC相当但未超越，且两者在样本外均受识别墙限制。在路径依赖权益任务中情况反转：基于同一欧式曲面校准后，仅用边际分布的方法存在结构性缺陷（ATM远期起始期权定价误差约为+100%），而XiNet的单一自洽测度将偏差控制在+0.3%，优于最大熵WMC（偏差为-24%），原因在于ξ=f_θ(路径特征)能捕捉欧式期权无法约束的联合结构。因此，识别具有风险特异性，XiNet是一种可整合可用工具并一致定价所有权益的单一测度。
英文摘要
In incomplete markets, no-arbitrage (NFLVR) guarantees the existence, not the uniqueness, of an equivalent local martingale measure (ELMM): unhedgeable risks (jumps, stochastic volatility) admit a whole family of equivalent measures, and asset dynamics alone cannot pin down the one the market selects. We characterize the identifiability of $Q$ from option data and propose a measure that is identifiable from data yet prices any claim consistently. The key boundary is an ``identification wall'': European options identify only the terminal marginal, while out-of-sample tails and path/joint structure require instruments matched to the priced risk (variance or higher-moment swaps, path-dependent claims). Within this view, minimum-relative-entropy weighted Monte Carlo (WMC) is the optimal baseline for the marginal; we generalize it to a full path-space measure change parameterized by a neural network on physical scenarios---XiNet---which learns $ξ=\mathrm{d}\mathbb{Q}/\mathrm{d}\mathbb{P}$ directly from 8 model-free path features, with option prices as a soft constraint. On European (marginal) pricing XiNet matches but does not surpass WMC, and both are bound by the identification wall out-of-sample. On path-dependent claims the picture reverses: calibrated on the same European surface, per-marginal methods fail structurally (an ATM forward-start is mispriced by $\sim+100\%$), whereas XiNet's single self-consistent measure keeps the bias to $+0.3\%$, beating maximum-entropy WMC ($-24\%$), because $ξ=f_θ(\text{path features})$ captures joint structure Europeans cannot constrain. Identification is thus risk-specific, and XiNet is a single measure that absorbs available instruments and prices all claims consistently.
