XVA computed directly from a Monte Carlo Expected Exposure profile produced by your internal system. No exposure approximation is made on this side — all six components use EE(t) and ENE(t) as inputs directly.

Present value of expected loss from counterparty default. Always negative — a cost to you.

Mirror of CVA. Applied to ENE — exposure where you owe money to the counterparty. DVA is a gain: it increases when your own creditworthiness deteriorates. Required under IFRS 13, controversial in practice.

FCA is the cost of funding the uncollateralised positive MTM. FBA is the benefit when negative MTM means the counterparty is effectively funding you. Always shown separately — never netted without disclosure.

ColVA is omitted. USD cash-only CSA has no cheapest-to-deliver optionality so ColVA = 0 exactly. For uncollateralised client trades use No CSA (factor = 1.0).

MVA is the SIMM IM cost on your inter-dealer hedge, not the client trade. The client trade has no CSA; you post IM on the hedge.

Discretization convention

CVA and DVA use right-endpoint EE(t_i) -- the standard discrete approximation assuming default occurs at the end of each time step. FCA, FBA, and KVA use the trapezoidal average (EE(t_{i-1}) + EE(t_i)) / 2 because these costs accrue continuously over [t_{i-1}, t_i]. For i=0 the previous EE is taken as zero (zero exposure at trade inception). For sparse EE schedules (annual points), the trapezoidal correction on FCA/FBA is typically 3-8% relative to the right-endpoint approximation.

Cost of funding SIMM Initial Margin posted on your inter-dealer hedge. IM sits in a segregated account earning near-zero — the opportunity cost is your FTP rate.

Present value of the cost of holding regulatory capital against the trade at your institution's hurdle rate. The bank must hold CET1 equity capital against every derivative position. That capital cannot be deployed elsewhere — its opportunity cost is h per year. KVA is the PV of that ongoing drag for the full life of the trade. It is a real economic cost even though it never appears as a direct cash flow.

Framework 1: SA-CCR (Basel III -- current standard for most banks)

Standardised Approach for Counterparty Credit Risk, mandatory for IRB banks since 2017 (BCBS 279). SA-CCR replaced CEM as the standard EAD calculation method for OTC derivatives. The EAD formula is: EAD = alpha x (RC + PFE), where alpha = 1.4, RC = replacement cost (current MTM floored at zero), and PFE = potential future exposure computed from supervisory delta x supervisory factor x adjusted notional x maturity factor. For this tool, MC EE(t) serves as a combined proxy for RC + PFE, so the 1.4 alpha is applied directly to EE(t).

M=1.0 when EE comes from your MC system for the actual trade (default, recommended). The MC simulation already ran the asset class risk -- FX volatility for a XCCY swap, rate vol for an IRS. The EE profile already reflects the correct exposure for that instrument. Applying M>1 on top of MC EE double-counts the asset class risk and overstates KVA materially (8x for FX). Example: a XCCY swap where MC EE = $14M, M=1.0 gives KVA EAD = 1.4 x $14M = $19.6M, which is already higher than the SA-CCR regulatory EAD of ~$5.6M ($100M x 4% x 1.4). Conservative but not absurd.

M>1 only when proxying -- EE from a different asset class than the trade. If you computed EE for an IR swap but want to estimate KVA for an FX trade, scale by M = SF_FX / SF_IR = 8.0. This is a proxy-of-a-proxy used when you cannot run MC for the actual instrument.

M_asset values below are reference only. Apply them only in the proxy case above. For own-MC-EE trades, always use M=1.0 regardless of asset class.

Framework 2: CEM (Basel II / Current Exposure Method -- legacy)

The Current Exposure Method was the Basel II standard for derivatives EAD prior to SA-CCR. Some jurisdictions and smaller institutions still use CEM, particularly where SA-CCR has not yet been mandated. CEM EAD = max(MTM, 0) + Add-on, where Add-on = Notional x CCF. The CCF (Credit Conversion Factor) is a flat percentage of notional that proxies potential future exposure. It varies by asset class AND by residual maturity -- this is the key difference from SA-CCR.

Since this tool uses EE(t) from MC rather than notional, M_asset under CEM is normalised as M = CCF_asset / 0.50%, where 0.50% is the 1-5Y IR CCF used as a consistent cross-band baseline. This ensures M=1.0 for vanilla IR trades in the standard 1-5Y tenor bracket. The alpha factor is set to 1.0 under CEM (no separate alpha multiplier exists in the CEM formula).

The tool auto-selects the tenor band from the last time point in your EE profile and auto-populates M accordingly. For IR <= 1Y the CCF is 0% -- CEM treats short-dated IR as having no PFE add-on. The tool floors M at 1.0 in this case since current exposure still exists via MTM.

CEM vs SA-CCR: key differences

1. Discount Factors -- Log-Linear on Zero Rates

Between bootstrapped tenor points, zero rates are linearly interpolated. The discount factor is then exp(-z x t). This is the standard OIS curve convention -- it produces smooth positive forward rates.

2. CDS Survival Probability -- Piecewise Constant Hazard

The hazard rate is held constant between CDS tenor points. This is the ISDA and Bloomberg CDS bootstrap convention. It produces a monotonically decreasing survival curve. The key convention: CDS(t_i) is the par spread for the interval [t_{i-1}, t_i]. CDS_1Y applies over [0, 1Y], CDS_2Y over [1Y, 2Y], CDS_3Y over [2Y, 3Y], and so on. Hazard rate in each segment is approximated as CDS(t_i)/(1-R), which is exact for constant intensity and a good approximation for most IG/HY spreads at standard tenors.

3. FTP Curve -- Linear on Spread

Par swap rates are stripped into zero rates using standard annual coupon bootstrap. Short end (money market) uses zero = par directly. Annual swap tenors are bootstrapped iteratively.

For a trade with flat (constant) expected exposure E0, flat hazard rate lambda derived from a flat CDS spread s, flat recovery R, and flat discount rate r, CVA has the following analytical solution. Use this to verify the tool against known inputs.

Benchmark test: set EE = $1,000,000 flat across all time steps, ENE = 0, CDS = 100bp flat (all tenors), Recovery = 40%, OIS = 4.0% flat (bootstrap from par rates or paste DFs). T = 5Y. Expected CVA = -(0.60) x 1,000,000 x (0.01667 / (0.01667 + 0.04)) x (1 - exp(-0.05667 x 5)) = approximately -$131,000. The tool should match within 1% for this case -- any larger deviation indicates a discretization or interpolation issue.