How is the Default Risk Charge calculated under FRTB, and how does it differ from the old incremental risk charge?

The Default Risk Charge (DRC) under FRTB captures the jump-to-default (JTD) risk of traded credit instruments — the sudden loss when an issuer defaults. It replaces the Incremental Risk Charge (IRC) from Basel 2.5 with a more comprehensive framework.\n\nKey Differences from IRC:\n\n| Feature | IRC (Basel 2.5) | DRC (FRTB) |\n|---|---|---|\n| Scope | Bonds, CDS | All instruments with default risk |\n| Horizon | 1 year, constant level of risk | 1 year, constant positions |\n| Confidence level | 99.9% | 99.9% |\n| Migration risk | Included | Excluded (captured in ES) |\n| Equity default | Not covered | Covered via equity JTD |\n| Hedging recognition | Full | Constrained by maturity mismatch |\n\nDRC Simulation Steps:\n\n1. Compute JTD amounts for each position:\n - Long bond: JTD = Notional x LGD (loss given default)\n - Short CDS protection: JTD = -Notional x LGD (hedge)\n - Equity: JTD = Market Value (total loss in default)\n\n2. Assign default probabilities based on credit rating:\n\n| Rating | 1-Year PD |\n|---|---|\n| AAA | 0.03% |\n| AA | 0.06% |\n| A | 0.10% |\n| BBB | 0.30% |\n| BB | 1.20% |\n| B | 3.50% |\n| CCC | 10.0% |\n\n3. Simulate correlated defaults using a multi-factor Gaussian copula with:\n - Systematic risk factor loadings based on industry and region\n - Idiosyncratic risk component per issuer\n - Default occurs when the latent variable falls below the PD threshold\n\n4. Calculate portfolio loss for each simulation trial\n5. Determine 99.9% quantile of the loss distribution over 10,000+ simulations\n\nWorked Example:\nHedgeworth Securities holds:\n- Long $20M Hartland Corp bond (BBB, LGD 60%): JTD = $20M x 0.60 = $12M\n- Short $15M Hartland CDS protection: JTD = -$15M x 0.60 = -$9M\n- Long $8M Eastwick Inc bond (BB, LGD 65%): JTD = $8M x 0.65 = $5.2M\n\nNet JTD on Hartland: $12M - $9M = $3M (partially hedged)\nNet JTD on Eastwick: $5.2M (unhedged)\n\nAfter simulation (10,000 trials, asset correlation 0.25):\n- Mean loss: $0.18M\n- 99.9% loss: $8.9M (both issuers default in stress scenario)\n\nDRC = $8.9M\n\nHedging Recognition Constraints:\n- Long/short positions on the same obligor may offset\n- Maturity mismatches between bond and CDS reduce hedge effectiveness\n- Index hedges provide only partial offset against single-name positions\n- Systematic hedges (shorting an index) are recognized at a reduced correlation-based benefit\n\nDeepen your understanding of credit risk capital in our FRM Part II course.