# FRTBTrace

Exact trade-level attribution of FRTB-IMA capital. A QRS@NTU research project (Quantitative Research Society, Singapore; Nanyang Technological University).

- Overview: https://qrsntu.org/projects/frtbtrace/
- How it works: https://qrsntu.org/projects/frtbtrace/details/
- Paper (arXiv 2609.32238): https://arxiv.org/abs/2609.32238

Plain-text summary for AI agents and readers, generated from the evidence file behind the pages; the pages are the full account. This is research software on synthetic books, not a regulatory method.

## Design

FRTBTrace attributes market-risk capital under the internal-models approach of the Fundamental Review of the Trading Book (FRTB-IMA) to individual trades. Instead of one attribution vector reused for every purpose, it types the question first: marginal impact, removal effect, accounting allocation, historical origin or hedge choice. The full capital calculation (expected shortfall, stress ratio, non-modellable and default-risk charges, history maxima, standardised-approach comparison) is written as a graph over (observation date, trade) positions. After one forward evaluation that records the active branch at every nonsmooth node, one reverse pass propagates allocations by local Euler rules, giving a ledger that adds up to the computed capital K under stated homogeneity assumptions. Removal and hedge-choice questions are answered by exact revaluation, and ties are flagged instead of being reported as a unique marginal.

## Key results

- Synthetic, pre-registered benchmark of 60 books: 42 small tie books (36 built on a kink) and 18 main books of 96 trades.
- On the 14 smooth main books, 21-99% of capital (median 61%) sits on past observation dates, outside any sensitivity to today's book.
- The accounting and origin ledgers reconcile to the engine's own capital within relative error 5.6e-16 (tie books) and 4.3e-16 (main books).
- A finite-difference check of the origin ledger over all 80,640 (date, trade) positions of the smooth main books: 80,630 agree within 1e-8 at relative step 1e-6; the other 10 straddle a branch change and agree within 1.4e-9 at step 1e-7.
- Six published allocators and a numerical Euler control each answer at most 2 of the five questions; FRTBTrace answers every question the benchmark defines an answer for. Shapley values over trades have no answer on these books.

## Limitations

- Every book is synthetic, including the standardised-approach, non-modellable and default inputs, with a fixed 1.5 multiplier and at most 96 trades.
- Exactness is relative to the implemented calculation and its allocation rule; it is not a regulatorily prescribed attribution. There is no independent second implementation of capital K, and several agreement checks are referenced to the engine itself.
- At ties the engine returns one flagged representative of the marginal set, not the complete set; the realisable set is built only on the small tie books.
- A frozen remainder exists only while an averaged history branch binds, as it does on all 14 smooth main books, so the past-date share describes that regime and the synthetic generator, not a typical bank.
- Shapley values are never computed: "no answer" rests on the benchmark's domain convention for small sub-books.
- No authoritative timing exists, so no speed claim is made.
- An exploratory agent prototype (12 runs of one model on 9 calibration books) scored 94/94 with the engine against 76/94 without; the gap is the 18 desk-accounting items and is fixed by the study design.

## Not claimed

- No regulatory or prescribed attribution: the ledger is exact relative to the implemented calculation and its allocation rule.
- No result on real bank portfolios: every book is synthetic, with synthetic standardised-approach, non-modellable and default inputs.
- No speed or scaling claim: no authoritative timing was obtained.
- No evaluation of FRTBTrace inside a deployed AI agent; the agent interface is proposed, and only a command-line prototype exists.
- No claim that the published allocators are wrong on the questions they were designed for; the comparison is about which questions each one answers.

## Papers

- Exact Trade-Level Attribution of FRTB-IMA Capital. arXiv 2609.32238, 26 September 2026.
- Auditable FRTB Capital Explanations: A Tool Contract for Financial AI Agents. Yuhe Sui. Workshop on Responsible AI Operations for Finance (RAIOps4Fin), ICAIF 2026: accepted.
- What Post-hoc Attributions of FRTB-IMA Capital Answer. Yuhe Sui, Yingzhi Tang. Workshop on Interpretability and Alignment in Financial Models (IAFM), ICAIF 2026: accepted.

## A question to start with

Explain the five attribution questions to a risk manager, then give the three strongest criticisms of the evidence and one experiment that would settle each.