Industry: Banking and Financial Services
Product: ModelRisk
Application: CVA / DVA on a Vanilla Interest-Rate Swap Book

A $40M XVA Reserve the Spreadsheet Couldn't See: CVA/DVA on a $28B Swap Book

Under Basel III FRTB and CVA capital rules, every uncollateralised OTC derivative trade carries a Credit Valuation Adjustment (CVA) charge in addition to its mark-to-market value. A regional bank running a $28B notional, mostly-vanilla interest-rate swap book with 47 corporate counterparties had been booking CVA via a closed-form proxy that took counterparty PD and average swap PFE and multiplied them together. The proxy gave a CVA reserve of $11M. A full Monte Carlo XVA simulation gave $40M - a 3.6x understatement, driven by the right-way / wrong-way risk between counterparty creditworthiness and the same yield-curve moves that drove swap exposure.

The XVA desk replaced the proxy with a Vose Software ModelRisk simulation that priced CVA, DVA and the funding adjustment (FVA) jointly on a coherent set of forward yield-curve scenarios and counterparty credit paths.

CVA = sum over time of E[ EE(t) dPD(t) ] (1 - R)

The CVA formula reads simply enough:

CVA = (1 - R) integral_0^T EE(t) dPD(t)

where EE(t) is expected positive exposure at time t and dPD(t) is the marginal default probability between t and t+dt. The closed-form proxy uses averages. The Monte Carlo engine simulates the joint distribution.

• Forward yield curve — Hull-White 1-factor (mean-reversion 0.08, vol 1.1%) calibrated to the SOFR curve and the swaption surface. 25,000 paths, 60 monthly time steps over 5 years average swap tenor.
• Per-counterparty credit spread — each of the 47 counterparties' 5-yr CDS spread modeled as a CIR process with long-run mean equal to the current spread and vol 18% of level. Default time is the first jump of a Cox process with intensity proportional to spread.
• Wrong-way risk — for each receive-fix counterparty, the correlation between the counterparty's credit spread and the relevant swap rate was modeled at +0.35 (rates up -> swap PFE for receive-fix down and counterparty credit spreads tighten - benign). For pay-fix counterparties the correlation is -0.35 (rates up -> swap PFE for pay-fix up and spreads widen - the wrong-way case).
• Netting and collateral — exposures aggregated within each ISDA netting set; CSA thresholds and minimum transfer amounts applied path-by-path so the collateral mechanics are realistic, not assumed away.

The closed-form said $11M. The simulation said $40M.

The top 12 counterparties account for 84% of total CVA. The single largest CVA at $8.7M sits on a high-yield energy corporate with $2.1B notional of pay-fix swaps - a wrong-way position. The proxy under-stated it by 4.1x. Pay-fix exposures to BB-rated names dominate the right tail. The benign net-receive book on investment-grade names actually generates positive DVA (own-credit benefit) that reduces the total: gross CVA $52M, DVA $12M, net XVA reserve $40M.

Expected exposure has a distribution, not a curve

The deterministic EE profile is a single rising-then-falling curve - the classic "swap PFE bell." The Monte Carlo simulation tells a sharper story: because the median rate path keeps the pay-fix swap close to par, the P50 EE peaks at barely $0.1M - essentially flat - while the exposure lives entirely in the right tail, with the P95 EE peaking at $39.5M and the P99 EE at $56.1M, both around the 3-year mark. CVA is integrating EE under each path's default time, not under the average path - which is why averaging EE and averaging PD and multiplying loses most of the answer.

What actually drives total CVA

The largest CVA driver is the wrong-way correlation on pay-fix BB names: $8.6M of CVA swings on the rho parameter alone. Recovery rate (range 25%-50%) is second ($5.4M). The Hull-White vol parameter is third ($4.1M). Counterparty credit-spread vol is fourth ($3.2M). The closed-form proxy is dimensionally blind to the first three of these - it treats them as scalars rather than as joint distributions, which is why it under-counts CVA by a factor of three.

What the model changed

• XVA reserve grew from $11M to $40M, reported to risk and finance as a one-time catch-up; future quarterly XVA accruals run off the Monte Carlo engine.
• Three pay-fix wrong-way exposures unwound - the top three CVA contributors had a combined $19M CVA and $7M of expected fee margin; the trades were a net negative.
• The CVA hedge program shifted from credit-index hedges to single-name CDS on the top eight CVA-contributing counterparties, cutting CVA P&L vol by 41% at the same notional hedge cost.
• A two-way CSA was renegotiated on the highest-PFE corporate counterparty, eliminating $4.8M of CVA at zero P&L cost.
• CVA capital charge under FRTB-CVA moved from the standardised approach to the basic approach with internal-model approval, lowering RWA on the swap book by $310M.

ModelRisk Functionality Used

• Hull-White 1-factor term-structure simulation (mean-reversion 0.08, vol 1.1%) on 25,000 paths * 60 monthly steps that produced the full distribution of per-counterparty exposure under coherent yield-curve scenarios.
• CIR credit-spread processes per counterparty (vol = 18% of level) with default modeled as the first jump of a Cox process, so default time is correlated with the spread path it sampled.
• Wrong-way correlation +/-0.35 between credit-spread shocks and swap-rate shocks per counterparty type, surfacing the $8.6M wrong-way premium the closed-form proxy assumed at zero.
• Netting-set and CSA-aware exposure aggregation that respected thresholds and minimum transfer amounts path-by-path - producing CVA that responded to collateral changes, not just to gross PFE.
• DVA and FVA layered on the same paths, so total XVA ($52M CVA - $12M DVA = $40M reserve) was internally consistent rather than three separate proxies that don't add up.

A vanilla swap is not a vanilla risk: CVA is a non-linear integral against a correlated credit and exposure path, and Monte Carlo is the only valuation framework that lets the integrand be what the integrand actually is.