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.

Key Differences from IRC:

Feature	IRC (Basel 2.5)	DRC (FRTB)
Scope	Bonds, CDS	All instruments with default risk
Horizon	1 year, constant level of risk	1 year, constant positions
Confidence level	99.9%	99.9%
Migration risk	Included	Excluded (captured in ES)
Equity default	Not covered	Covered via equity JTD
Hedging recognition	Full	Constrained by maturity mismatch

DRC Simulation Steps:

1. Compute JTD amounts for each position:

   • Long bond: JTD = Notional x LGD (loss given default)
   • Short CDS protection: JTD = -Notional x LGD (hedge)
   • Equity: JTD = Market Value (total loss in default)

2. Assign default probabilities based on credit rating:

Rating	1-Year PD
AAA	0.03%
AA	0.06%
A	0.10%
BBB	0.30%
BB	1.20%
B	3.50%
CCC	10.0%

3. Simulate correlated defaults using a multi-factor Gaussian copula with:

   • Systematic risk factor loadings based on industry and region
   • Idiosyncratic risk component per issuer
   • Default occurs when the latent variable falls below the PD threshold

4. Calculate portfolio loss for each simulation trial

5. Determine 99.9% quantile of the loss distribution over 10,000+ simulations

Worked Example: Hedgeworth Securities holds:

• Long $20M Hartland Corp bond (BBB, LGD 60$20M x 0.60 = **$12M**\n- Short$15M Hartland CDS protection: JTD = -$15M x 0.60 = -$9M
• Long $8M Eastwick Inc bond (BB, LGD 65$8M x 0.65 = **$5.2M**\n\nNet JTD on Hartland:$12M - $9M =$3M (partially hedged) Net JTD on Eastwick: $5.2M (unhedged)\n\nAfter simulation (10,000 trials, asset correlation 0.25):\n- Mean loss:$0.18M
• 99.9% loss: $8.9M** (both issuers default in stress scenario)\n\nDRC = **$8.9M

Hedging Recognition Constraints:

• Long/short positions on the same obligor may offset
• Maturity mismatches between bond and CDS reduce hedge effectiveness
• Index hedges provide only partial offset against single-name positions
• Systematic hedges (shorting an index) are recognized at a reduced correlation-based benefit

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