# Economic specification of the funding book

As of 19 September 2026. This is a fictional USD book and a public contract for its standalone numerical verifier. It is not a production installation, an observed transaction, or a national regulatory opinion. The exact source requests are preserved in [user-request.xml](../sources/user-request.xml) and [source-structures.xml](../sources/source-structures.xml). The transaction and event evidence is in [exhibit-fields.md](exhibit-fields.md); the connected episodes and their boundaries are in [world-topology.md](world-topology.md). The accepted economic corrections are specified below, with the detailed capital and accounting conventions in [capital-rulebook.md](capital-rulebook.md), [capital-actions.md](capital-actions.md) and [reserve-module.md](reserve-module.md).

The book retains the requested USD1bn, twenty-year funding against five-year EM deployment. It does not turn that mismatch into a fully hedged trade. The corrections below distinguish a funding opportunity from an enforceable claim, an accounting charge from cash expenditure, and capital capacity from money available to settle a payment.

## 1. Evidence, units and numerical ownership

The transaction documents, quote sheets, curve observations, legal opinions, event notices and ledger openings in [case-exhibits.json](../fixtures/case-exhibits.json) are fictional public exhibits. [numerical-inputs.json](../fixtures/numerical-inputs.json) is the canonical numerical input. Amounts there are USD, rates are decimal fractions, and times are years unless a field explicitly specifies business days. Tables below use USD millions where stated.

Official rules are identified by paragraph and dated source in [capital-rulebook.md](capital-rulebook.md) and [valuation-capital-annex.md](valuation-capital-annex.md). Pricing curves, the quarter grid, quote conversion, recoveries, joint stresses, funding facilities and the 10% capital price are synthetic assumptions. Arithmetic implied by those assumptions is a calculated illustration, not evidence of observed market calibration. A legal or accounting conclusion requires the supplied opinion and its covered facts. An unresolved condition remains unresolved rather than receiving a numerical default.

The implementation boundary is explicit:

- `numerical_fixture.compute_core(parameters)` produces marks, sensitivities, CVA, capital profiles, KVA, priced actions and the allocation solution.
- `reserve_ledger.simulate_cash(parameters, reference_credit_move, funding_move, own_spread)` produces actual quarterly cash, title and financing consequences.
- `reserve_ledger.compute_reserves(parameters, core)` produces the management reserve schedules, attribution and independent accounting bridge.
- `validate_exhibits.validate_bundle(root)` checks the public case envelope and references before any report is graded. Missing required facts raise `ReferenceError`; they are not a candidate's scored economic mistake.

Displayed numerical results come from the original flat-bundle execution snapshots [core-results.json](../evidence/baseline/core-results.json) and [reserves-results.json](../evidence/baseline/reserves-results.json). [numerical-anchors.json](../evidence/baseline/numerical-anchors.json) and [action-anchors.json](../evidence/baseline/action-anchors.json) collect the relevant baseline outputs. Formulas below define the calculations; the output files retain their precision. Recognised incurred CVA is explicitly zero in the base capital calculation. None of these computed outputs is an input exposure path or evidence of real-world calibration. Historical output hashes do not attest the organized files' changed paths.

## 2. Both legs, including the source of principal

### 2.1 Contract terms

| Quantity | Public assumption |
|---|---|
| Funding notional and opening reference value, N | USD1,000,000,000 |
| Funding maturity | 20 years, 80 quarterly settlement periods |
| Deployment maturity | 5 years, 20 quarterly interest periods and bullet repayment |
| Numerical period, delta | 0.25 year |
| OIS, r | 4% nominal annual, compounded quarterly for this calculation |
| Initial internal AAA composite spread, b0 | 20bp, including its disclosed desk add-on |
| Executed financing margin over b0 | 50bp |
| Locked financing spread over OIS, k | b0 + 50bp = 70bp; subsequent b moves do not reset k |
| Matching replacement quote margin over b | 80bp in the synthetic joint quote process |
| Initial matching replacement spread, m0 | b0 + 80bp = 100bp over OIS |
| U reference coupon | OIS + 100bp, initially 5% annually |
| EM deployment coupon | OIS + 400bp, initially 8% annually |
| Funding provider CDS and recovery | 80bp; 40% recovery in the disclosed flat-hazard illustration |
| Own unsecured bond spread | 50bp initially; 150bp in the selected funding stress |
| Own CDS spread | 30bp initially, independently specified |
| Opening legacy borrowing | USD1bn, at OIS, still outstanding after the new funding transaction |
| Opening freely usable cash | USD100m before the separately identified day-one fee |

U is an already-issued, ordinary AAA financial floating-rate note. Meridian initially owns it. Meridian sells legal title to U to the funding provider P and receives its total return back under the twenty-year TRS. Meridian is total-return receiver and financing payer. The sale supplies USD1bn; the unfunded derivative supplies no second principal.

The EM borrower receives the USD1bn sale proceeds. Its loan is separate from the TRS and from P. Deployment collateral, U, and CSA collateral held against P are three different legal objects. U held by P is not collateral received by Meridian against P's default.

The calendar-based confirmations use their stated day counts, resets and settlement dates. The numerical proof uses the disclosed exact quarter grid. It does not silently claim that every dated quarter is 0.25 under ACT/365F.

### 2.2 Opening cash and statutory balance sheet

The table is before fees, reserves and subsequent market movements. Amounts are USD millions.

| Stage | Cash | Statutory assets other than cash | Statutory liabilities | Equity | Legal effect |
|---|---:|---|---|---:|---|
| Opening | 100 | U 1,000 | Legacy borrowing 1,000 | 100 | Meridian owns U |
| Sale of U to P settles | 1,100 | U 1,000 retained for accounting | Legacy borrowing 1,000; new financing liability 1,000 | 100 | Title to U passes to P; sale proceeds arrive |
| TRS execution | 1,100 | No duplicate statutory derivative for the retained rights | Existing financing remains | 100 | Meridian receives U's return and pays financing; no new principal |
| EM advance settles | 100 | U 1,000; EM advance 1,000 | Legacy 1,000; financing 1,000 | 100 | EM borrower receives 1,000; security rights arise only as documented |

The same-transferee sale plus full return retention fails derecognition in this case. [IFRS 9, 2026 issued edition][IFRS9], paragraphs 3.2.15, B3.2.14 and B3.2.16(o), supports retention of U and recognition of the financing liability without recognising the same rights again as a derivative. Legal ownership and accounting recognition therefore differ. Paragraph 3.2.22 also prevents treating the accounting asset and associated liability as an automatically net presentation.

The USD1m day-one fee is an actual setup-service fee, expensed and paid after the sale and deployment settle. It reduces unrestricted cash to USD99m and statutory equity to USD99m before management X. It is not assumed to be a lifetime financing fee eligible for capitalisation. The payment has its own source entry; it cannot be hidden in a noncash reserve or represented as a second funding advance.

The explicit fictional regulatory classification letter separately selects SA-CCR for the legal TRS and the relevant written-credit leverage treatment. That selection is not an inference from IFRS, and it does not permit a second statutory asset. Without the classification letter, derivative versus financing/SFT treatment needs adjudication before those capital formulas can be used.

### 2.3 Quarterly return and financing cash

Let p_j be U's ex-distribution price per unit of face and let the opening price be 1. Equivalently, use the identified quantity Q_U and currency price P_j with Q_U P_0 = N. The formulas below use the normalised price. Let d_j be the distribution per unit of face and p_last the reference price from the last actual settled return reset.

```text
TRS_cash_j = N * (d_j + p_j - p_last)
             - N * delta_j * (OIS_j + k)

For a surviving ordinary quarter:
    d_j = delta_j * (OIS_j + 0.01)

At U's final redemption:
    p_j = 0
    d_j = delta_j * (OIS_j + 0.01) + 1
```

The final price is zero because the note has redeemed; its principal is already in d_j. Adding another N receipt or payment to this return formula would double count principal. A payment instruction is not an actual reset until the specified settlement has occurred. Unpaid return, accrued financing and a disputed amount remain in the close-out valuation.

At unchanged par and OIS, quarterly TRS cash is USD0.750m and annual TRS cash is USD3m. The EM loan pays USD20m quarterly for five years, and the legacy borrowing costs USD10m quarterly. Whole-book quarterly operating cash before cash-account interest, new borrowing, fees and hedges is therefore USD10.750m during the first five years. The USD3m annual TRS amount is a funding-only panel, not the full book's annual income.

The cash ledger books U's coupon through P's TRS remittance once. The statutory ledger can show U income and financing expense, but it cannot also add a second direct cash coupon from U's issuer to Meridian.

Interim reference-price return settlements change cash and the retained-sale financing balance. A negative price return is a payment to P and reduces that financing balance; U is separately revalued under the identified accounting policy. The cash repayment itself is not another expense on top of U's valuation loss. A positive return reverses the direction. The financing coupon still follows its fixed notional and executed spread unless an actual amendment changes those terms.

### 2.4 Year five and year twenty

At year five the performing EM borrower repays USD1bn. The base reinvestment instruction places that principal in an OIS account through the remaining fifteen years. It does not assume another EM loan at the original 400bp margin. Interest on that OIS principal offsets the OIS cost of the USD1bn legacy borrowing in the unchanged-rate base case. Funding TRS cash, provider exposure and capital continue.

The desk can select a different reinvestment only with a new executable quote, credit decision, funding use and legal agreement. The price and availability of that future investment are the reinvestment risk. Five-year amortisation or five-year protection does not close the twenty-year funding position.

At year twenty:

1. U redeems to its legal holder P. The last TRS return uses `d = coupon + 1`, `p = 0`, and the actual last reset price. The net price/redemption component is `N * (1 - p_last)`, not another unqualified N.
2. The retained-asset and financing ledger records U's redemption and the corresponding extinction of the financing balance. In the performing par endpoint, the final price-return adjustment brings that balance to N before P's redemption extinguishes it. This is not a second cash withdrawal from Meridian.
3. The parked EM principal becomes available to repay the separate legacy borrowing. Any real additional liquidity borrowing is repaid from available cash under its own terms.
4. Fees, margin returns, hedges, disputes and close-out receivables settle separately. An unresolved USD0.500m provider claim and its USD0.500m reserve in the terminal exhibit survive contractual maturity. Age alone does not erase either.

[reserve-module.md](reserve-module.md) specifies these postings and the independent closing-balance derivation. A terminal zero is valid only for obligations actually discharged.

## 3. E1: funding benefit, legal value and reference return

### 3.1 Quote-conditioned valuation

Define the numerical discount and annuity for h remaining years on the quarter grid:

```text
D_r(h) = (1 + r * delta)^(-h / delta)
A_r(h) = sum_j=1..h/delta delta * D_r(j*delta)
       = (1 - D_r(h)) / r
```

The synthetic replacement quotation supplies a linear spread-to-price conversion with `A_quote = A_0.04(h)`. This annuity is a disclosed quote convention, not a universal law for all funding trades. Off quarter dates, `off_quarter_convention=fractional_remaining_annuity_clean_quote` explicitly extends `(1-D_r(h))/r` using the fractional power above; it is not the sum of the original contract's irregular coupon cash flows. A quote could instead supply its own PV01 or an upfront price for the old locked spread, but those alternatives require their own implemented terms.

For a reset-to-today replacement quote with the same U, quantity, notional, maturity, cash-flow terms, legal rights, collateral basis and cost basis:

```text
F_quote(t) = N * [m_reset(t,h) - k] * A_quote(t,h)

Reference_adjustment(t)
    = D(t, next_actual_settlement) * N * [p_U(t) - p_last_actual]

V_legal(t) = F_quote(t) + Reference_adjustment(t) + unsettled_stubs(t)
```

The stubs include any separately stated unpaid return, accrual or contractual close-out item not already included in the quote. Base clean-reset observations explicitly set them to zero. Unknown stubs do not default to zero. Rolled calls to `funding_mark` require explicit `next_payment_delay` and `unsettled_stub`; a pending same-day price settlement uses delay zero. The inception default reads the required `funding_contract.next_price_settlement_years` rather than deriving a new quarter from remaining tenor. Scheduled-zero-tenor marks do not extinguish pending settlement claims.

A quotation on the original reference basis already includes the old-reference adjustment. In that alternative, use its direct old-contract value or its stated conversion and do not add `p_U - p_last` again. Quote matching requires the actual remaining contract, not a generic twenty-year financing spread from another provider.

The desk also computes a management funding opportunity from its internal composite b plus its desk margin. An internal curve change cannot create a claim on P. In this synthetic case, separately supplied replacement quotes happen to follow `m_reset = b + 80bp`. That is a joint assumed quote process. It is not an internal-b-linked termination payoff invented in the contract.

At a matched, post-settlement reset with zero stubs and matching costs/basis, the internal funding opportunity can equal F_quote and V_legal. Outside those conditions the three are distinct. Missing or mismatched executable quotation evidence raises a reference-input error. It never licenses substituting the internal opportunity for CCR exposure or using V = 0.

The quotation's fictional executability does not itself satisfy the IFRS day-one observable-input test. Accounting observability has separate evidence and a prior unit-of-account gate.

### 3.2 Reference pricing and numerical anchors

For the public flat snapshot, U's current OIS coupon is held fixed while the credit-yield spread is shocked. With `c_U = 0.04 + 0.01 = 0.05`:

```text
p_U(h, x_U) = c_U * A_(c_U+x_U)(h) + D_(c_U+x_U)(h)
```

This is a synthetic yield-based mark of the promised reference cash flows. It is not a provider-default model. If OIS changes, coupon resets and discounting must be recomputed from the actual floating-rate terms rather than treating this snapshot formula as a fixed-rate contract forever.

At inception, after a matched reset, `m0 - k = 30bp`. Known calculated anchors are:

| Item | Quarterly convention | Continuous comparison, not used by the verifier |
|---|---:|---:|
| Twenty-year annuity | 13.722051526 years | 13.766775897 years |
| Funding benefit at 30bp, USDm | 41.166154579 | 41.300327691 |
| Funding spread DV01, USDm per bp | 1.372205153 | 1.376677590 |
| Increment for a 100bp funding-quote widening, USDm | 137.220515265 | 137.667758971 |

The raw request's approximately USD41m and USD138m are sound order-of-magnitude diagnostics under their stated annuity. They are neither regulatory constants nor substitutes for full V.

The following controlled observations keep twenty years remaining and the old actual price at 1. They use the next-quarter discount on the unsettled reference adjustment:

| Joint observation | Funding component, USDm | Full legal value before return settlement, USDm |
|---|---:|---:|
| No curve move | 41.166155 | 41.166155 |
| Replacement quote +100bp, U credit unchanged | 178.386670 | 178.386670 |
| Replacement quote +100bp, U credit +25bp | 178.386670 | 147.850900 |
| Replacement quote +100bp, U credit +100bp | 178.386670 | 63.517057 |

The reference-loss offset is an economic component of V, not CSA collateral and not a regulatory haircut benefit. After the reference loss settles, its old-reference adjustment disappears from V because cash has moved, while the surviving fixed financing advantage remains. A reference-price reset is not a full fair-value reset of the whole TRS.

The funding trade is therefore an asset in the selected positive-value states, not in every state. A sufficiently adverse U move or a tightening replacement funding quote can make full V negative. A 100bp tightening with U unchanged produces a USD96.054361m payable under the same twenty-year quote conversion.

### 3.3 Exposures are derived, never supplied

The current positive legal exposure is `max(V_legal, 0)` before the relevant collateral/default-recovery treatment. The SA-CCR calculation then uses the full contractual V with the applicable legal C, replacement-cost formula and add-on. A positive funding opportunity alone is not EAD.

For CVA, the public quarter-end-after-payment convention supplies the default timing. In the flat provider illustration:

```text
lambda_P = provider_CDS / (1 - recovery_P)
S_P(t) = exp(-lambda_P * t)

CVA = sum_j D_OIS(t_j) * (1 - recovery_P)
            * [S_P(t_(j-1)) - S_P(t_j)]
            * E[positive close-out exposure at t_j | P defaults there]
```

Each conditional close-out exposure is repriced from the same contract, reference price/reset state and applicable collateral recovery. Default observations remain the original funding quarter ends even when a capital action becomes effective between them; the exposure at a default date uses the action status then. An execution date changes capital accrual, not the default clock. A remaining tail begins with the stub to the next original funding payment. The base post-settlement illustration reduces exposure to the surviving funding component; that simplification follows from the stated event ordering and reference state. A default before settlement, a correlated U shock, a dispute or non-reusable collateral requires the corresponding full calculation. No exhibit supplies EE, EPE, an exposure vector or an answer-shaped reserve schedule.

Provider CDS of 80bp with 40% recovery gives the illustration's hazard `0.008 / 0.6`. The provider CDS cannot be replaced by the internal AAA curve, U's rating, the desk's own CDS or an unrelated EM spread. A deterministic W stress is not by itself a calibrated joint default probability model.

## 4. E4 and the mismatch: distinct curves and basis risks

| Curve or observation | What it drives | What it does not establish |
|---|---|---|
| OIS and its forecast/reset convention | Discounting, floating coupons, cash remuneration and the quoted annuity conversion | Provider credit quality or a supervisory 5% decay |
| Internal AAA financials CDS composite plus desk add-on, b | Internal replacement-funding opportunity and the disclosed funding-allocation sensitivity | An enforceable claim, a provider CDS curve, or U's issue rating |
| Independently supplied matching replacement quotes, m | Quote-supported old-contract financing value | Automatic IFRS observability or an internal-curve termination right |
| U issuer credit/yield curve | U's price, unsettled return, and reference-credit risk | Collateral C received from P or P's default probability |
| Funding provider P CDS | Provider survival/default loss in CVA | Actual own borrowing cost or U's supervisory factor |
| Own unsecured bond funding curve | The rate on actual own cash borrowing and its premium over the chosen cash benchmark | A borrowing need caused by a noncash mark |
| Own CDS | Own credit diagnostics and the bond-CDS basis | A substitute loan quote; zero cash cost when CDS is used |
| EM borrower credit/yield curve | EM valuation, credit loss and reinvestment economics | An own-funding-induced change to the borrower's contractual coupon |
| Deployment collateral issuer curve and price | Realisation value and collateral price risk | Automatic rating migration, supervisory haircut or eligibility |
| CSA remuneration and collateral/FX basis | Net economics of cash collateral, currency conversion and funding | Permission to reuse segregated collateral |
| Protection seller H CDS and hedge terms | H's default risk and the separately calculated protection economics | Netting H with P or automatic CVA hedge designation |
| Market financing haircut and spread schedules | Cash advance and lender-specific financing price | Supervisory mitigation or a spread mechanically determined by the haircut |

Two curves may co-move in a scenario without becoming the same input. In W3, the internal quote driver, own bond spread, provider CDS and EM spread are shocked jointly, while own CDS remains separately stated. The internal-to-quoted-replacement basis, internal-to-own-bond basis, U-to-internal-AAA basis, EM-to-own-funding basis, bond-CDS basis and collateral-remuneration/FX basis must therefore remain visible.

At inception, own bonds are OIS + 50bp and own CDS is 30bp. Their 20bp difference is the bond-CDS basis. The actual premium for borrowing at the bond curve and placing the proceeds at OIS is 50bp, not 20bp. A basis-only adjustment is possible only after specifying a benchmark that already charges the own-credit component. It cannot be added on top of the full 50bp or described as a universal pure-liquidity cost. Using own CDS as a cash funding curve is wrong, but it does not mathematically set all funding cost to zero.

### 4.1 Funding spread duration versus contractual loan value

The requested long-twenty/short-five sensitivity is a funding-allocation comparison. For the disclosed matched annuity convention:

```text
Funding_spread_DV01 = +N * A_0.04(20) * 0.0001
Five_year_deployment_funding_allocation_DV01
                   = -N * A_0.04(5) * 0.0001
Net_funding_allocation_DV01
                   = N * [A_0.04(20) - A_0.04(5)] * 0.0001
```

Known anchors are +USD1.372205153m, -USD0.451138824m and +USD0.921066328m per bp. The five-year magnitude is disclosed separately from its negative position sign in the report.

This does not mean that an EM borrower's legal debt reprices when Meridian's internal funding spread changes. Its contractual coupon and principal remain the same. Its independent credit-mark snapshot uses:

```text
c_EM = 0.04 + 0.04 = 0.08
p_EM(h, x_EM) = c_EM * A_(c_EM+x_EM)(h) + D_(c_EM+x_EM)(h)
```

The marked loan value is `N * p_EM`; the funding-allocation debit is a management comparison, not another loan asset or an extra cash expense. The selected W3 first-quarter observation has h = 4.75 and x_EM = 0.03. The resulting price loss is noncash unless the loan is sold, margined or otherwise contractually cash-settled.

Funding spread DV01 is also not OIS DV01. Holding m and k fixed under the quote conversion:

```text
dA_r(h)/dr = -sum_j=1..h/delta j * delta^2
                         * (1+r*delta)^(-j-1)
dF_quote/dr = N * (m-k) * dA_r(h)/dr
```

An actual OIS scenario also changes forward coupons, cash returns and any quoted conversion or basis. Both legs' resets must be respected. The supervisory duration with 5% exponential decay in SA-CCR is neither this rate derivative nor the OIS annuity.

### 4.2 Collateral price, rating and the two haircut systems

Reprice collateral from its own curve. Separately apply a dated issue-rating or eligibility event, issuer type, residual maturity, legal rights, positive-correlation test and the applicable holding-period haircut. The sequence is then current recognised mitigation, exposure, RWA, allocated capital, KVA and the client price needed to cover that cost.

A spread movement is not itself a rating instruction. Conversely, a rating event can change a haircut or remove recognition with no contemporaneous market-price movement. Under the selected rating-permitted banking-book Basel comparator, a sovereign issue requires at least BB-, not investment grade in every case. The chosen B-rated own-sovereign paper fails both the rating test and the independent same-issuer correlation test. See CRE22.7, CRE22.34, CRE22.45 and CRE22.49 in [capital-rulebook.md](capital-rulebook.md).

The market haircut determines how much cash a lender advances. The supervisory haircut determines eligible regulatory mitigation or posting exposure. They are distinct inputs with separate tenors and purposes. The empirical short-dated findings in S3 motivate lender segmentation and concentration constraints, not a calibration of five- or twenty-year EM financing. A higher safe-collateral haircut-to-volatility ratio refutes a universal proportional-volatility rule; it does not prove that nominal haircuts decrease with volatility. [allocation-episode.md](allocation-episode.md) contains the separate seven-day executable allocation.

## 5. E2, E3 and A3: when a funding cost actually exists

### 5.1 Actual cash deficits, not stock-mark borrowing

For each settlement time, `simulate_cash` starts with the accessible cash account and applies contractual receipts and payments in the specified netting order. It includes deployment coupon/principal, net TRS return and financing, legacy interest, fees, margin, hedges, actual loss payments and any existing facility interest. It does not put V, D, X, EAD, AVA or capital release in the cash account.

```text
Cash_before_new_financing_j
    = available_opening_cash_j + accessible_settled_receipts_j
      - contractual_cash_payments_due_j

Required_new_cash_j = max(0, -Cash_before_new_financing_j)
Actual_draw_j = min(Required_new_cash_j, usable_executed_facility_capacity_j)
Residual_shortfall_j = Required_new_cash_j - Actual_draw_j
```

A fully available facility can fund the deficit; a proposed, inaccessible or insufficient facility cannot. Positive cash can repay existing draws according to the documented sweep and buffer policy. Borrowing changes cash and a debt principal account. Only its interest and fees are expenses.

The actual annual loan rate is OIS plus the quoted own unsecured bond spread. The incremental funding-premium diagnostic uses that spread above the stated OIS benchmark. Total contractual interest still appears in the cash and statutory ledger. If borrowed money funds an external OIS deposit, the deposit's actual interest offsets the OIS component. If it funds a cash loss instead, there is no invented matching deposit income.

A 100bp move only in the matching funding quote produces a larger noncash mark and potentially larger CVA/KVA deductions. With no other cash obligation it creates no additional borrowing, so the base mark-only UFVA is zero. A noncash XVA expense likewise reduces management equity without creating a cash payable. This refutes the unconditional reserve-implies-borrowing recursion in A3.

The actual positive-deficit experiment instead shocks U credit by 250bp before the first quarterly return settlement. The contractual reference loss is paid to P. The own-bond premium is then 150bp on the resulting actual draw. Its path is `compute_reserves(...)["cash_scenarios"]["actual_reference_credit_widening_250bp"]`, not the size of the reserve. The common funding-only shock, the actual reference-loss scenario and the separately opt-in experiment below must not be added together as though they were one financing need.

The executed scenario draws USD145.7623083242m at the first settlement and has USD3.7104953200m present value of the actual borrowing premium over OIS. Its all-in contractual borrowing-interest PV is separately USD13.6051495067m. These are `summary.PV_actual_funding_spread_cost` and `summary.PV_actual_borrowing_interest` in that cash scenario. The mark-only scenario's actual UFVA is zero; the opt-in external-deposit experiment below produces USD17.9588363722m. They are three different cash contracts/states, not alternative estimates of one cost.

This executed-cash path is a counterfactual conditional on the book having been lawfully funded and approved. It does not establish that the proposed book's opening eligible capital satisfies the whole-book constraints in section 7. A capital deficit requires rejection or a separately evidenced capital transaction before execution, not a fictional Tier 1 top-up. Within that explicitly conditional path, the reference settlement and resulting borrowing are real cash obligations, unlike the noncash reserve balances.

### 5.2 The conditional quadratic experiment and the USD14.5m claim

The public `conditional_reserve_facility` is a separate sensitivity experiment, not an automatic feature of the base book. An effective external facility borrows at own bonds and places money in a segregated OIS deposit. Its expressly selected target is the positive incremental quote-supported funding benefit caused by a move x, excluding the original 30bp benefit. The quote has its own `scenario_margin_beta=beta_quote` and `conversion_rate=r_quote`. Its assumed own-spread response is independently `s_own = s0 + beta_own*x`. The canonical values are s0 = 50bp, beta_quote = beta_own = 1 and r_quote = OIS = 4%; their equality is a fictional common-factor/conversion assumption, not an identity between distinct curves.

For the executed facility, beginning-quarter deposit balances and end-quarter interest charges give:

```text
z(x) = max(beta_quote * x, 0)
L_j(x) = N * z(x) * A_r_quote(20 - (j-1)*delta)

I_quote = N * sum_j=1..80 delta * D_OIS(j*delta)
                                 * A_r_quote(20 - (j-1)*delta)

UFVA_conditional(x) = I_quote * z(x) * (s0 + beta_own*x)
```

Under the canonical values, `I = I_quote = 119725575814.7565`. With spreads expressed as annual decimal rates, its units are USD times years squared. At x = 0.01, the result is USD17.958836372m. Its linear contribution is `I*0.005*x`; its quadratic contribution is `I*x^2`. The second term exceeds the first once x exceeds 50bp in this particular experiment. Altering the quote beta or conversion rate changes the target and coefficient in both the analytic result and cash ledger; it does not change OIS expense discounting. An unexecuted facility has zero primary borrowing, cost and fee.

The prompt's estimate `70m * 1.5% * 13.8 = 14.49m` is arithmetically consistent with those rough inputs. It is not the result of the selected amortising quarter-grid balances. Their discounted average incremental balance is `I*0.01/A_0.04(20)`, approximately USD87m rather than USD70m. Obtaining USD14.5m would require a different exposure average, timing, survival weighting, spread benchmark or funding contract. The verifier must state that difference, not tune an undisclosed exposure path to the desired number.

The quadratic result applies only while the positive-balance branch is active and only under the stated beta and funding transaction. Floors, defaults, collateral availability and finite facility capacity can change that shape. A claim that all uncollateralised receivables have this UFVA is false.

### 5.3 Executing a CSA changes rights and cash

An enforceable two-way daily cash-VM agreement can reduce unsecured close-out loss and SA-CCR exposure. Whether received VM reduces a funding need depends on its settlement, currency, accessibility, reuse rights and remuneration. The economic condition for combining it with an external-deposit experiment would be:

```text
Unfunded_target = max(0, required_external_deposit
                        - settled_legally_reusable_VM_available_for_that_use)
```

Do not reuse the same VM against two needs. Segregated cash, unreceived calls and securities the bank cannot monetise by the deadline do not pay today's obligations. VM is collateral with a return obligation, not income. Threshold, MTA, NICA, disputes and MPOR still matter; zero replacement cost is not zero PFE.

The implemented conditional experiment explicitly requires `reusable_VM="0"`; it rejects a nonzero amount. It does not implement the combined formula above or infer reusable cash from the separate CSA action. A joint VM/prefunding process needs its own dated cash-rights and allocation contract before that boundary can be exercised.

The adverse-VM action snapshot is separate from the opening USD100m cash book. It supplies a USD20m available buffer and a USD100m executable line. The binding quote in [capital-actions.md](capital-actions.md#executable-terms-and-timing) charges USD1m for CSA execution, USD0.100m for facility setup, USD0.050m annual fixed commitment, USD0.025m annual administration and another 10bp annually on the USD100m line. The annual quoted charges therefore total USD0.175m; omitting the setup, administration or limit-based charge understates the cost.

The immediate-execution static comparator for the 100bp tightening is USD96.0543606853m VM, leaving USD76.0543606853m beyond the buffer; the static VM field is `actions.CSA.normal.instantaneous_stress_VM`. The actual quoted action takes effect after two business days, at model year 0.008. Repricing then gives USD96.0292195555m VM and a USD76.0292195555m facility draw, respectively `actions.CSA.normal.executed_stress_VM` and `actions.CSA.normal.facility_draw`. The static and executed amounts are not interchangeable observations.

For the executed 30/365-year draw, gross facility interest is USD0.3436937322m, buffer OIS opportunity cost is USD0.0657534247m and VM remuneration is USD0.3157125026m. Their net cost is USD0.0937346542m, with PV USD0.0933987733m. Adding the upfront-cost PV of USD1.0996498041m and running-cost PV of USD2.3999728785m gives total quoted cost PV USD3.5930214559m. The immediate static draw's roughly USD0.09376565m spread cost is only its comparator, not the delayed action's cost. Received-margin relief in one state does not erase posting risk in another.

Thus E3 is retained as a legal-and-operational sensitivity, but rejected as a universal equivalence between no CSA and positive UFVA, or between a signed CSA and no funding cost. A CSA may reduce capital while making liquidity worse.

## 6. E5 and A1-A5: two management pots and one P&L

### 6.1 Sign convention and attribution

Use gain-positive clean values G and hedge values H, and deduction-positive deferral D and XVA reserve X. Let C be cash, M other nonoverlapping assets, and B liabilities. A management risk ledger can be represented as:

```text
Equity_management = C + M + G + H - B - D - X
```

Every position must have one representation in that ledger. The retained U/financing statutory accounts and a management replacement benefit require an explicit bridge; adding both as independent statutory fair-valued positions would duplicate rights. [reserve-module.md](reserve-module.md) separates the funding-only panel, the full cash book and the statutory bridge.

For a priced trade panel, after separating unrelated book movements and capital transactions:

```text
PnL = CF_G + (G1-G0) + CF_H + (H1-H0)
      - actual_funding_expense - other_expense
      - (D1-D0) - (X1-X0)
```

Use frozen opening market inputs to compute the time-only roll values G_roll, D_roll and each X_roll. Apply observed market changes next, and effective structural actions last. This ordering is public and prevents the same release from being classified twice.

```text
Carry = CF_G + G_roll - G0
Clean_market_move = G_pre_action - G_roll
Hedge_PnL = CF_H + H1 - H0

For each deduction R, where R is D or an X component:
    Reserve_theta_R = R0 - R_roll
    Reserve_market_move_R = R_roll - R_pre_action
    Reserve_action_release_R = R_pre_action - R1
```

A documented observability release of D is separate from spread-driven X remeasurement and from routine time release. Effective structural actions also include their clean settlement value and quoted fees; the reserve credit alone is not the action's net economics.

Expected theta is P&L once. It is part of earning the initially priced risk premium, not additional new profit on top of the change in the reserve. Spread-driven release is also P&L and can reverse. An unhedged market gain is not fee income. The raw sentence that every term except carry is a reserve movement is too broad: actual hedge gains, clean market changes and cash funding expense are not automatically reserve movements.

A release of a future-funding-cost reserve as cost is consumed must be paired with the corresponding actual funding expense. Booking only the release invents profit. Conversely, charging both the already-priced reserve consumption and a second reserve for the same cost duplicates the expense.

Debt draws/repayments, VM transfers, principal repayment and capital issuance are not trade P&L. A new cash loss, interest, fee or hedge payment has its own source entry. The verifier must derive the independent journal and closing assets/liabilities from those sources and compare their equity movement with attribution. Defining closing equity as opening equity plus the reported P&L is not a check.

### 6.2 Pot D and the accounting-unit gate

For management only, the initial gross benefit is deferred on a frozen price-time schedule:

```text
D_management(0) = N * 0.003 * A_0.04(20)
D_management_roll(t) = N * 0.003 * A_0.04(20-t)
```

The original spread advantage and conversion are frozen for this schedule. A tightening current spread does not release D; nor does a widening current spread replenish it. Evidence that a previously unobservable pricing factor has become observable can support an additional release under the applicable policy. Arbitrary straight-line amortisation is not substituted for the priced time factor.

For statutory recognition, identify the accounting unit before applying the day-one test. The base failed-sale unit contains retained U and its financing liability, so it does not first book a USD41m standalone derivative gain and then decide whether to defer it.

For a genuinely separate qualifying instrument, IFRS 9 paragraphs 5.1.1A and B5.1.2A distinguish an active-market identical price or a valuation using only observable-market data from other valuations. The latter initially defers the difference from transaction price, then recognises it only as arising from changes in factors, including time, that market participants consider in pricing. The relevant IFRS edition is the [2026 issued text][IFRS9]. This is not a rule that all internal inputs are always unobservable, or that one fictional quote makes all inputs observable.

A separate numerical unit example makes the netting point explicit. Suppose a valid standalone unit has clean value USD41m, applicable statutory valuation adjustments USD12m, and transaction price zero. Its net fair value is USD29m. If the day-one exception fails, the deferred difference is USD29m, not a gross USD41m deferral plus an immediate USD12m loss on the same unit. The management gross D and management X pots therefore need a bridge to statutory accounting rather than a claim that both are mandatory IFRS liabilities. Management KVA is not automatically a statutory fair-value adjustment.

### 6.3 Pot X, the corrected capital basis and worked time/market panels

```text
X = CVA + actual_cash_based_FVA_UFVA + KVA + other_explicit_reserves
```

Fees paid as expenses are not added again as a reserve unless the stated policy first reserves a future unpaid fee and releases it against settlement. The components keep separate time, market, effective-action and consumption movements.

For the following funding-only panel, quote and U are at a matched reset, no hedge is executed, actual additional funding is zero, and no other reserve is silently added. Define the capital and CVA quantities exactly through the public core API:

```text
C0 = core["funding"]["normal"]["CVA"]
K0 = core["funding"]["normal"]["KVA"]
C1 = core["funding"]["year1_roll"]["CVA"]
K1 = core["funding"]["year1_roll"]["KVA"]
Cs = core["funding"]["year1_stress"]["CVA"]
Ks = core["funding"]["year1_stress"]["KVA"]
X0 = C0 + K0
X1 = C1 + K1
Xs = Cs + Ks
```

These K values use recognised incurred CVA equal to zero. Earlier illustrative KVA values that subtracted an unrecognised management CVA reserve from default-risk EAD are superseded. CRE51.12 permits the qualifying incurred write-down, not an arbitrary management reserve. A separate recognised-write-down countercase must state its statutory basis and cannot be the default.

Amounts in the next table are USD millions, rounded from the executed core and reserve outputs; API values are in USD. The named C/K/X definitions above identify the exact source fields.

| Funding-only item | Inception | One-year frozen-market roll | Instantaneous shock after that roll |
|---|---:|---:|---:|
| Remaining funding life | 20 years | 19 years | 19 years |
| Gross F at matched reset | 41.166154579 | 39.792364782 | 172.433580720 |
| D management | 41.166154579 | 39.792364782 | 39.792364782 |
| Provider CDS | 80bp | 80bp | 160bp |
| Change in replacement funding spread from inception | 0bp | 0bp | +100bp |
| CVA | 2.601931020 | 2.414305784 | 19.440057857 |
| KVA, corrected no-incurred-write-down basis | 27.523018931 | 24.702391545 | 62.236661004 |
| Total X | 30.124949951 | 27.116697329 | 81.676718861 |
| TRS cash received during the panel | 0 | 3.000000 | 0 |
| Newly created cash borrowing from the mark/charge | 0 | 0 | 0 |

At inception, the priced net management benefit before deferral is `F0-X0-fee = USD10.0412046285m`. With gross management D equal to F0, the initial management charge is `-X0-fee = -USD31.1249499510m`. The independent opening journal therefore leaves management equity of USD68.8750500490m from USD100m, while statutory equity is USD99m after the actual USD1m service expense. Neither the priced benefit nor the management charge is automatically statutory day-one P&L; the failed-sale accounting unit recognises no separate funding-opportunity gain.

The one-year frozen-market panel is fully specified by:

```text
Carry = 3.000000 + 39.7923647816 - 41.1661545794
      = 1.6262102022 USDm
D_theta = 1.3737897978 USDm
X_theta = X0 - X1 = 3.0082526224 USDm
Funding_panel_PnL = Carry + D_theta + X_theta
                  = 3.000000 USDm + X0 - X1
                  = 6.0082526224 USDm
```

These values are `management_scenarios.one_year_roll.funding_component.attribution` in the reserve output. The independent ledger, not the attribution identity, supplies the reconciliation evidence. The expected release is counted once. The separate whole-book panel includes EM carry, legacy interest and OIS cash interest: its first-year management P&L is USD50.6773603624m after the already expensed day-one fee, with management equity moving from USD68.8750500490m to USD119.5524104114m. Its funding-only USD6.0082526224m is not an additional whole-book profit line.

The instantaneous market panel changes no time, payment or D. Its result is:

```text
Clean_market_move = 132.6412159387 USDm
Reserve_market_move = X1 - Xs = -54.5600215322 USDm
Instantaneous_PnL = Clean_market_move + Reserve_market_move
                  = 78.0811944065 USDm
Cash_change_from_this_mark_and_reserve_remeasurement = 0
```

This is the required divergence of the two pots: D stays on its old priced schedule while X remeasures to changed provider credit and funding exposure. The instantaneous panel's independent journal and equity change both give USD78.0811944065m; no cash or new borrowing appears. The corresponding `compute_reserves` panels are `management_scenarios.opening`, `management_scenarios.one_year_roll` and `management_scenarios.instant_funding_100bp_provider_80bp`. The 81-row `reserve_schedule` includes opening and quarterly observations through contractual year twenty; the separate terminal settlement state retains any unresolved claim.

### 6.4 A4: reserve uncertainty and available CET1

The [valuation-capital annex](valuation-capital-annex.md) uses identified recognised fair-value exposures and an expressly selected EU-style model-risk core method. Its two current-model exit-cost ranges are USD1.75m to USD4.25m and USD1.375m to USD2.625m. Expected costs are USD3m and USD2m; separately identified same-source accounting prudence is USD0.2m and USD0.1m. The 90th-percentile costs are USD4m and USD2.5m. Residual uncertainty is therefore USD0.8m and USD0.4m. Method 1's 50% factor gives an incremental AVA of USD0.6m.

That component reduces available CET1 from USD12m to USD11.4m in the explicitly controlled USD100m fixed-RWA illustration. It is not a cash outflow or trading P&L. The separate assumption of USD0.6m replacement equity held for twenty years at a 10% annual charge gives:

```text
KVA_AVA = 0.10 * 0.600m * A_0.04(20)
        = 0.8233230916m
```

This is a controlled replacement-equity component, not the whole book's KVA and not an amount to add if the same capital use is already priced. Shifting expected exit cost while holding uncertainty width and same-source prudence fixed can leave AVA unchanged. A wider uncertainty range can increase AVA without a larger expected reserve. The raw automatic chain from larger reserve level to larger AVA is therefore conditional, not a rule.

The applicability and dates are those of CRR consolidated 26 June 2026 and the identified RTS consolidated 26 June 2020, with the post-2020 50% factor. These sources do not make the fictional institution EU-regulated or turn a management funding opportunity into an in-scope accounting asset.

## 7. Capital cost and the defined comparison with UFVA

The detailed regulatory formulas and rejection gates remain in [capital-rulebook.md](capital-rulebook.md). The funding baseline uses credit-primary SA-CCR, AAA reference SF 0.38%, a twenty-year supervisory duration, alpha 1.4, no CSA collateral and provider A-category ECRA risk weight 30%. The legal classification also requires a dual credit/interest-rate countercase; a trade name cannot settle its primary-driver assessment.

For the selected standalone one-provider reduced-BA panel:

```text
K_funding_CCR_CVA(t)
    = 0.08 * RWA_funding_CCR(t) + K_BA_CVA(t)

KVA_funding(h)
    = 0.10 * sum_j delta * D_OIS(j*delta)
                     * K_funding_CCR_CVA(h-(j-1)*delta)
```

Capital is sampled at the beginning of the quarter and priced at its end. No recognised incurred CVA write-down is deducted in the base. The KVA path is the disclosed survival-conditional allocation through maturity; default-weighted CVA and the no-default conditional prefunding experiment have their own stated measures. They cannot be silently presented as one empirically calibrated expectation.

For an action, the charge intervals are split only at the genuine execution, expiry and recognition events specified in [capital-actions.md](capital-actions.md#executable-terms-and-timing). Both comparators use the same knots and pay at original quarter ends. Additional reporting observations evaluate current capital but do not resample that accrual basis. The `_capital_action` keyword-only `observations` channel therefore changes the returned `observation_profile`, not cash schedules or KVA; `events` remains the genuine-pricing-event channel. Observation-density invariance under this fixed charge contract is distinct from, and does not establish, numerical convergence of a continuously accruing capital integral.

The executed normal standalone funding KVA is USD27.5230189305m. There are two different comparisons with the conditional USD17.9588363722m UFVA:

1. The stressed capital-cost level, `core["funding"]["mark_stress"]["KVA"]`, is USD69.4099354188m: 3.864946146 times conditional UFVA. This is the standalone funding CCR+CVA component for the 100bp quote move with provider CDS held at 80bp, the chosen reset convention and U otherwise unchanged.
2. The incremental capital cost is the stressed level minus `core["funding"]["normal"]["KVA"]`: USD41.8869164882m, or 2.332384773 times `core["conditional_UFVA"]["UFVA"]`. Comparing increments aligns the funding experiment more closely than comparing it with the whole stressed KVA level. The ratio fields are `core["sensitivities"]["standalone_total_KVA_to_conditional_UFVA_ratio"]` and `core["sensitivities"]["standalone_marginal_KVA_to_conditional_UFVA_ratio"]`.

Both comparisons support K8 only for that named component, scenario and allocation rule. They do not prove that KVA universally dominates actual funding cost. Actual mark-only cash UFVA is zero. The USD3.7104953200m actual borrowing-premium PV belongs to the separate reference-loss cash scenario, whereas USD17.9588363722m belongs to the conditional external-deposit contract. Substituting either cash number into the other scenario without repricing changes the comparison.

Whole-book capital must include retained U, deployment, cash, other applicable exposures, the legal TRS classification and written-credit leverage notional. The explicit controlled base weights are 20% on the retained AAA U, 100% on the unmitigated EM cash advance and 0% on the specified central-bank cash account, before adding the relevant funding CCR/CVA amounts. The earlier isolated USD90m risk-weighted capital snapshot is not the actual capital requirement of this USD1bn EM book. Even deployment and retained U alone contribute USD80m and USD16m of 8%-minimum capital at par.

The executed whole-book base requires USD135.6507222715m under the risk constraint, versus USD94.6989784923m under the 3% leverage constraint. Available Tier 1 after the paid service fee is USD99m, with no automatic AVA from the separate controlled example. Risk capital binds and the USD36.6507222715m shortage makes `executable_under_stated_capital` false in `leverage.actual_base_after_day1_fee`. The calculable cash path is therefore an existing-book/counterfactual exposure, not approval to book it without an evidenced capital transaction or effective restructuring.

The desk's disclosed minimum-only all-equity allocation compares `max(0.08*RWA_book, 0.03*L_book)` on the same with/without portfolio. This is an internal pricing convention, not a replacement for Basel's simultaneous CET1, Tier 1 and total-capital requirements. A collateral substitution can move the binding constraint to leverage. The five-year protection maturity ratio can be one at CDS execution despite the longer funding exposure; it does not confer a five-year-capped written-credit leverage offset. The immediate-execution twenty-versus-five comparator has a fifteen-year unprotected tail. The quoted action starts after two business days, expires at book year 5.008, and leaves 14.992 years after expiry plus an unprotected initial two-day interval.

[capital-actions.md](capital-actions.md) supplies executable quotes and lifetime comparisons for CSA execution, high-grade substitution, enforceable netting, designated or undesignated provider CDS, holding capital and releasing a substitution. The stated scopes matter:

- Substitution costs a 90bp annual concession on USD1bn for five years plus USD1m execution cost; undoing it costs USD0.250m. Reduced capital need not compensate for the lost yield.
- Netting costs USD0.750m and waits for the signed, scoped opinions and novation conditions. A pending thirty-business-day process provides no early relief.
- Five-year USD320m provider protection costs an 80bp annual premium, USD0.250m execution cost and USD0.025m annual administration. The five-year tenor runs from its actual two-business-day execution, not from book inception. Provider H's own exposure, CVA, designation, expiry and declining recognition remain in the before/after calculation; the full premium, fee and administration costs appear in [capital-actions.md](capital-actions.md).
- Holding capital costs the applicable KVA profile. Expected roll-down is already priced. Structural relief is the recalculated future-cost difference net of the action price, not an extra cash receipt.

Action NPVs labelled standalone CCR+CVA components do not become whole-bank gains merely because a separate leverage snapshot is shown. The allocation episode also supplies a concrete capital/economics reversal: routing all fifty small lots to the cheaper, weaker lender raises incremental SFT CCR capital versus the feasible forty-nine-lot alternative while lowering total financing cost. Capital capacity released by any action stays out of cash until an actual transaction changes cash.

If a five-year client spread is used to recover a selected cost NPV, the spread increment is `cost_NPV / [N*A_0.04(5)]` under this payment grid. Charging it over a fictional twenty-year deployment would understate the spread. The cost must include all relevant tail obligations and feasible execution costs on the stated allocation basis.

## 8. Public recomputation and report boundaries

| Obligation | Source facts and mechanism | Authoritative calculation |
|---|---|---|
| E1 | Sale/title, TR roles, issued U, reset price, matched replacement quote, stubs | `core.marks`; F, reference adjustment and V derived separately |
| E2 | Explicit cash obligations or the separately effective prefunding facility; own-bond quote and beta | Actual `cash_scenarios` versus `core.conditional_UFVA` |
| E3 | Executed CSA, direction, thresholds, remuneration, custody/reuse and settled transfers | Recomputed margin exposure and cash deficits, including adverse VM |
| E4 | Distinct curve identities and full before/after states | `core.curves`, `core.sensitivities`, CVA and cash-funding recomputation |
| E5 | Opening balances, sourced cash/title entries, clean marks, D and X conventions | `compute_reserves` attribution versus independently derived journal/equity |
| A1 | Accounting unit first, then actual input observability | Management/statutory bridge and legitimate D release trigger |
| A2 | Frozen-market roll and subsequent market/action revaluation | Separate D/X schedules and component attribution |
| A3 | Actual payment causing a deficit, no debt entry for a reserve alone | `simulate_cash`; separate cash-funding-expense line |
| A4 | Recognised FV scope, model uncertainty and same-source prudence | Incremental AVA and available CET1, distinct from P&L/cash |
| A5 | Reconciliation, fees/funding/hedges and surviving obligations | Independent closing accounts and terminal USD0.500m unresolved-claim reserve |

The candidate still reports `rates`, `credit_xva`, `capital`, `liquidity` and `accounting` separately under [report.schema.json](../schemas/report.schema.json). Shared causes must agree across sections. Funding spread sensitivity can drive quote-derived exposure and conditional UFVA under the named cash contract. Valuation uncertainty can reduce CET1 and change the cost of allocated equity. Separate fields do not make these independent economic decisions.

[wrong-way-branches.md](wrong-way-branches.md) specifies the five mutually exclusive case instances implementing W1's two instrument-existence alternatives and W2-W4. Missing quotation, legal scope, issuer kind, correlation fact, cash access, rating or event timing is a reference failure. Evidenced non-recognition or a documented zero cash recovery is a valid case result. The distinction prevents missing data from making the trade look safe.

[IFRS9]: https://www.ifrs.org/content/dam/ifrs/publications/html-standards/english/2026/issued/ifrs9.html