XVA Greeks and Sensitivities: CS01, IR01, FX01 with Claude AI (2026)

XVA Greeks and the CVA Desk Hedging Framework

CVA desks don't just calculate CVA as a number — they actively manage CVA as a portfolio. This means hedging the market risk embedded in CVA: as credit spreads widen, CVA increases (costing more capital and P&L); as interest rates move, the expected exposure profile changes; as volatility increases, the uncertainty in future exposure widens. The first task in managing this risk is measuring it — computing the XVA Greeks (sensitivities) that drive CVA P&L. The second task is hedging these sensitivities using CDS, interest rate swaps, and options.

Under FRTB-CVA (Basel IV), this sensitivity framework is also the basis for regulatory capital: SA-CVA capital is directly computed from CVA sensitivities, weighted by prescribed risk weights and correlation matrices. This means that improving the accuracy of XVA Greek calculations improves both hedging quality and capital efficiency simultaneously. Claude helps CVA analysts compute and interpret these sensitivities, build attribution frameworks, and understand hedge structures. See SA-CVA under FRTB for the regulatory capital applications and XVA Trading Desk AI for the broader workflow context.

CS01: Credit Spread Delta

CS01 (Credit Spread 01) is the change in CVA for a 1bp widening in the counterparty's credit spread — the most direct measure of counterparty credit risk sensitivity in the CVA book. CVA is approximately linearly sensitive to credit spreads because the probability of default is approximately linear in the credit spread (for short horizons and small spread levels): PD(t) ≈ s × t / LGD for small s × t. This makes CVA CS01 approximately proportional to the exposure-weighted average life of the netting set: CS01 ≈ CVA / (s × weighted_average_life).

CS01 is the primary input to CVA credit spread hedging: the desk buys protection on CDS referencing the counterparty with a notional scaled to offset the portfolio CS01. For a CVA with CS01 of −$8,000 per basis point (meaning CVA increases by $8K for every 1bp credit spread widening), the hedge needs to have a CS01 of +$8,000 — approximately $8,000 / (CDS DV01 per $1M notional) in single-name CDS notional.

• "CVA CS01 calculation for an IR netting set: We have a netting set with a BBB industrial counterparty (CDS spread: 90bps flat, LGD 60%). Three IRS trades: (1) pay-fixed 5Y IRS, $50M, MTM +$1.8M, EPE profile $2.2M average; (2) pay-fixed 7Y IRS, $30M, MTM +$1.2M, EPE profile $1.6M average; (3) receive-fixed 3Y IRS, $20M, MTM −$0.4M, EPE profile $0.3M average (net only for negative MTM). Net EPE: $3.8M. Current CVA: $135K. Calculate CS01: (1) analytically as ∂CVA/∂s ≈ LGD × ∑_t EE(t) × (∂PD_marginal/∂s) × Δt — derive ∂PD/∂s from the hazard rate model, (2) numerically by bumping the credit spread from 90bps to 91bps and recomputing CVA, (3) express CS01 in $/bp and as a percentage of total CVA, (4) compute the CS01 for each individual trade to understand concentration, (5) size the CDS hedge: what notional of 5Y single-name CDS (CDS CS01 approximately $450 per $1M notional) fully offsets our portfolio CS01?"
• "CVA CS01 sensitivity by tenor for SA-CVA: For SA-CVA capital calculation, we need CS01 broken down by the SIMM/SA-CVA credit spread tenor buckets (1Y, 2Y, 3Y, 5Y, 10Y, 30Y). Our netting set has CVA profile with exposures maturing across 1-10Y. Compute the CS01 vector by tenor bucket: (1) explain how the total CVA CS01 is decomposed into contributions from each time interval — the CS01 at tenor T_k is the change in CVA from bumping only the credit spread at that tenor, (2) construct a representative CS01 vector for a 3Y, 5Y, and 7Y pay-fixed IRS portfolio with $50M each, (3) explain why the 5Y bucket typically dominates for a standard corporate derivative book, (4) how does the SA-CVA capital formula use this CS01 vector — apply the prescribed risk weight (IG 5Y: 1.38%) and within-bucket aggregation."

IR01: Interest Rate Delta

CVA IR01 is less intuitive than CS01 but equally important for large derivatives books. The channel is indirect: expected exposure E[max(MTM, 0)] depends on the current MTM and the volatility of future MTM changes. For pay-fixed IRS, the current MTM is positive when rates are below the fixed rate — so as rates fall, the trade moves into the money and expected exposure rises. This means CVA has negative IR01 for pay-fixed netting sets (CVA increases when rates fall, creating a rates risk that must be hedged with receive-fixed swaps).

• "CVA IR01 calculation for a pay-fixed IRS netting set: We have a $100M pay-fixed 5Y USD IRS netting set with a BBB counterparty (CDS 90bps). Current rate is 4.55% (ATM). Current CVA: $185K. CVA IR01 calculation: (1) bump the USD 5Y SOFR swap rate by +1bp (to 4.56%), recompute the expected exposure profile — for a pay-fixed IRS, a rate increase reduces positive MTM (our fixed payment becomes less attractive), reducing EPE, (2) bump the rate by −1bp (to 4.54%), recompute EPE and CVA, (3) compute CVA IR01 as (CVA(rate+1bp) − CVA(rate−1bp))/2, (4) explain the sign: should CVA IR01 be positive or negative for a pay-fixed netting set, (5) what IRS trade (pay-fixed or receive-fixed) hedges this CVA IR01, and what notional?"
• "CVA IR01 curve decomposition for a mixed-currency book: We have EUR and USD IRS trades across multiple tenors. CVA has IR01 sensitivity to both USD and EUR rate curves. Breakdown of CVA IR01 by currency and tenor: USD: 2Y −$2.1K, 5Y −$8.4K, 10Y −$4.2K; EUR: 2Y −$1.1K, 5Y −$5.6K, 10Y −$2.8K. (1) What IRS hedge portfolio neutralizes the USD CVA IR01 — show the receive-fixed USD IRS notional needed at each tenor, (2) for EUR, design a similar hedge, (3) explain the cross-currency basis: if we use EUR/USD XCCY swaps to convert USD hedges, do we introduce any basis risk, (4) how does the SA-CVA framework treat the IR01 vector for capital purposes — what are the prescribed risk weights for the USD and EUR IR delta buckets?"

FX01 and Cross-Currency CVA Sensitivity

For netting sets containing cross-currency trades (XCCY swaps, FX forwards, deliverable FX options), CVA has FX sensitivity because the exposure profile is denominated in a foreign currency. A EUR-reporting bank with USD-denominated netting sets sees its CVA rise when USD appreciates (because the USD-denominated positive exposure translates into more EUR CVA). FX01 (sometimes called FX delta or FX vega) measures this sensitivity.

• "CVA FX01 for a cross-currency portfolio: A EUR-reporting bank has USD-denominated netting sets with a US corporate counterparty. Total CVA on the USD netting sets: $480K (USD). Current EUR/USD rate: 1.08. CVA in EUR: €444K. FX01 analysis: (1) CVA FX01 = ∂CVA_EUR/∂(EUR/USD) — calculate the EUR change in CVA if EUR/USD moves from 1.08 to 1.09 (EUR appreciates by ~1%) and CVA in EUR falls by approximately 1%, (2) compute FX01 in EUR per 1% FX move, (3) what is the hedge for this FX01 — a EUR/USD forward or FX swap, what notional and direction, (4) explain why cross-currency CVA FX01 is different from the FX risk of the underlying XCCY trade itself, (5) in SA-CVA, the FX risk class has a risk weight of 7.4% — apply this to our FX delta and compute the FX capital component."

CVA Vega and Options Exposure

When a netting set contains options (swaptions, FX options, equity options, caps/floors), CVA has vega sensitivity: implied volatility changes affect the expected exposure profile because higher volatility means wider distribution of future MTM values, increasing expected positive exposure. CVA vega is most significant for swaption-heavy books and equity derivative books. For interest rate options (caps, floors, swaptions), CVA vega is driven by the IR volatility surface; for FX options, by the FX vol surface.

• "CVA vega for a swaption book: We have a netting set containing: (1) long receiver swaption, 1Y into 5Y, $100M notional, IR vol 85bps normal (underlying ATM); (2) short payer swaption, 2Y into 7Y, $75M notional, IR vol 90bps; (3) long cap, 3Y, $50M notional, vol 88bps. CVA vega measures how CVA changes when implied vol increases by 1%. Higher vol → wider MTM distribution → higher EPE → higher CVA. (1) Qualitatively explain which options increase CVA vega and which reduce it, (2) compute CVA vega approximately: CVA vega ≈ ∂CVA/∂σ ≈ LGD × ∑_t PD(t) × ∂E[max(V(t),0)]/∂σ — for each option, ∂E[max(V,0)]/∂σ ≈ option vega (via Black's formula), (3) estimate the net CVA vega for the netting set, (4) what instrument hedges CVA vega — a swaption straddle (long both payer and receiver) provides pure vega exposure; size the hedge notional."

P&L Attribution and Hedge Effectiveness

P&L attribution is the practice of explaining each day's CVA P&L change in terms of the risk factors that drove it. A well-designed attribution should explain more than 95% of daily CVA moves through the main Greeks (CS01, IR01, FX01, vega, theta). The unexplained residual captures higher-order effects (cross-gamma, model errors, market data corrections) and should be small and mean-reverting if the Greeks are computed accurately and the hedge is effective.

• "CVA P&L attribution for a one-week period: Our CVA portfolio had these weekly P&L: CVA changed from $4.82M to $5.31M — a $490K increase (worsening). During the week: counterparty CDS spreads widened by 8bps (CS01 effect), USD 5Y rates fell 12bps (IR01 effect), EUR/USD weakened 0.6% (FX01 effect). Greeks at start of week: CS01 = −$15K/bp, IR01 = −$6K/bp, FX01 = +$28K per 1% EUR/USD move. Attribution: (1) calculate the CS01 P&L: CS01 × Δs = −$15K × (−8) = +$120K (spreads widening increases CVA, worsening P&L); (2) calculate IR01 P&L: IR01 × Δr = −$6K × (−12) = +$72K; (3) calculate FX01 P&L: FX01 × ΔFX = +$28K × (−0.6) = −$16.8K; (4) total attributed: $120K + $72K − $16.8K = $175.2K. Residual: $490K − $175.2K = $314.8K unexplained. (5) What explains the large residual — second-order effects, new trades, counterparty-specific credit events, or model recalibration?"
• "CVA hedge effectiveness assessment: We have been running a CVA hedging program for 6 months. Our hedges: $120M notional single-name CDS across 8 counterparties, plus $500M iTraxx Main 5Y bought protection. CVA Greek snapshot at program start: CS01 = −$28K/bp, hedge CS01 = +$25K/bp (hedge ratio 89%). Over 6 months, unhedged CVA P&L would have been −$1.85M (CVA widened as credit spreads widened). Actual CVA P&L after hedges: −$380K. Hedge gain: $1.47M. (1) Calculate the hedge effectiveness ratio (1 − |hedged P&L| / |unhedged P&L|), (2) decompose the residual $380K loss: how much is from the 11% unhedged CS01 gap, how much from IR01 (not hedged), how much from basis (our single-name CDS vs. iTraxx tracking error), (3) what additional hedge would have reduced the residual most — a 5Y USD IRS or a wider iTraxx hedge, (4) how does this hedge effectiveness documentation satisfy the FRTB hedge recognition requirements for SA-CVA?"