Credit Valuation Adjustment (CVA) & XVA Lab
Model OTC derivative counterparty credit risk, Expected Exposure profiles (EE, EPE, PFE 95th/99th), unilateral CVA, DVA, Bilateral CVA (BCVA), hazard rate curves, and ISDA Credit Support Annex (CSA) collateral netting thresholds.
Portfolio & Credit Inputs
$186,412
0.75% of notional (15.2 bps/yr)$62,137
Own credit default benefit$124,275
Net fair value adjustment$3,842,500
EPE: $1,420,100Quantitative Exposure & XVA Visualizer
Counterparty Credit Risk & XVA Decomposition
| Component | Analytical Equation | Value ($) | % of Notional |
|---|---|---|---|
| Risk-Free Portfolio PV | PV_rf (Base MTM) |
$2,500,000 | 10.00% |
| Credit Valuation Adjustment (CVA) | CVA = (1 - R_c) × ∫ Z(t) EE(t) dPD_c(t) |
-$186,412 | -0.75% |
| Debit Valuation Adjustment (DVA) | DVA = (1 - R_b) × ∫ Z(t) NEE(t) dPD_b(t) |
+$62,137 | +0.25% |
| Bilateral CVA (BCVA = CVA - DVA) | Net Credit Adjustment |
-$124,275 | -0.50% |
| Fair Risky Exit Value | PV_risky = PV_rf - BCVA |
$2,375,725 | 9.50% |
| CSA Collateral Protection Benefit | ΔCVA = CVA_uncollateralized - CVA_csa |
$0 (No CSA) | 0.00% |
CVA Sensitivity Matrix ($)
Bilateral BCVA Sensitivity Matrix ($)
Counterparty Credit Risk & XVA Framework
1. CVA Analytical Formulation
Credit Valuation Adjustment quantifies the expected loss from counterparty default across the life of an OTC derivative portfolio. In continuous-time formulation:
≈ (1 - R_c) × ∑ Z(t_i) × EE(t_i) × [Q_c(t_{i-1}) - Q_c(t_i)]
Where $Z(t)$ is the risk-free discount factor, $EE(t) = \mathbb{E}[\max(V(t), 0)]$ is Expected Positive Exposure, and $dPD_c(t)$ is the marginal default probability density of the counterparty bootstrapped from its market CDS spread.
2. DVA and Bilateral CVA (BCVA)
Under IFRS 13 / ASC 820 fair value accounting standards, derivative exit prices must reflect two-way default risk. Debit Valuation Adjustment (DVA) measures the value of the reporting institution's own default:
BCVA = CVA - DVA
PV_risky = PV_risk_free - BCVA
Where $NEE(t) = \mathbb{E}[\max(-V(t), 0)]$ is the Negative Expected Exposure (the counterparty's exposure to our bank).
3. Exposure Profiles: EE, EPE, and PFE
Unlike bonds where principal is fixed, OTC derivative exposure fluctuates with underlying market drivers:
EPE = (1 / T) × ∫ EE(t) dt
PFE_α(t) = Notional × [μ·t + z_α × σ√t]
For interest rate and cross-currency swaps, the exposure profile typically exhibits a classic "diffusion hump" that rises with $\sqrt{t}$ early in the trade before amortizing toward zero at maturity.
4. ISDA CSA Collateral Netting Mitigation
Credit Support Annexes mitigate CVA by mandating collateral transfers whenever portfolio positive mark-to-market exceeds an uncollateralized Threshold ($H$):
CVA_mitigation = (CVA_uncoll - CVA_csa) / CVA_uncoll
Standard regulatory Margin Period of Risk (MPOR) is 10 to 20 days. Effective collateral agreements typically reduce total CVA capital charges by over 80%.