FRTB-IMA资本的精确交易级归因
Exact Trade-Level Attribution of FRTB-IMA Capital
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- Quantitative Research Society, Singapore（新加坡定量研究学会）
- Nanyang Technological University, Singapore（南洋理工大学）
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中文总结 AI 辅助
本文提出一种计算图与反向传播相结合的精确归因方法，将FRTB-IMA资本按观测日期和交易进行分配，确保对账一致，并识别监管平局下的边际顶点。
中文摘要 AI 辅助
交易账簿基本审查的内部模型方法（FRTB-IMA）在银行获批交易台的聚合层面确定市场风险资本，但并未说明该资本费用应如何归因于单个交易。风险管理者、资本规划者和验证者通常需要这种归因，而获取它却很困难：资本经过预期缺口、压力缩放、不可建模、违约风险、历史以及标准化方法等多个非光滑且依赖于过去头寸的层级。我们提出了一种将FRTB-IMA资本归因于（观测日期，交易）头寸的公式完备方法，该方法与计算出的资本对账一致。该计算被表示为计算图；在一次前向评估后，单次反向传播通过局部欧拉规则（预期缺口对偶权重、下限和最大值处的活跃分支权重、违约分位数情景）将分配向量传播至每个节点，从而避免了对每笔交易重新评估资本。在所述同质性假设下，分类账可证明地加总至资本以及任何交易台或产品分组，并且在光滑点等于欧拉（梯度）分配；它相对于已实现的计算和该规则是精确的，而非监管规定的归因。其过去日期的条目捕获了分配给较早观测日期的资本，而今日账簿的敏感性通过光滑点处的精确恒等式会遗漏这些。在监管平局（边际不唯一）的情况下，我们报告可实现边际顶点，通过精确线性规划测试识别，而非单一选择。在14个光滑的96笔交易合成基准账簿上，分配给过去观测日期的资本份额中位数为61%（范围21%-99%），分类账对账相对误差在5.6e-16以内。
英文摘要
The internal-models approach of the Fundamental Review of the Trading Book (FRTB-IMA) determines market-risk capital at the aggregate level of a bank's approved trading desks, but it does not say how that charge should be attributed to individual trades. Risk managers, capital planners and validators often need one, and it is hard to obtain: capital passes through expected-shortfall, stress-scaling, non-modellable, default-risk, history and standardised-approach layers that are nonsmooth and depend on past positions. We present a formula-complete attribution of FRTB-IMA capital to (observation date, trade) positions that reconciles to computed capital. The calculation is written as a computational graph; after one forward evaluation, a single reverse pass propagates allocation vectors through every node by local Euler rules (expected-shortfall dual weights, active-branch weights at floors and maxima, the default-quantile scenario), avoiding one capital re-evaluation per trade. Under stated homogeneity assumptions the ledger provably sums to capital and to any desk or product grouping, and equals the Euler (gradient) allocation at smooth points; it is exact relative to the implemented calculation and this rule, not a regulatorily prescribed attribution. Its past-date entries capture capital allocated to earlier observation dates, which today's-book sensitivities miss by an exact identity at smooth points. At regulatory ties, where the marginal is not unique, we report the realisable marginal vertices, identified by exact linear-programming tests, instead of one selection. On 14 smooth 96-trade synthetic benchmark books, the median share of capital allocated to past observation dates is 61% (range 21%-99%), and ledgers reconcile to within 5.6e-16 relative error.
