How do the threshold and minimum transfer amount in a CSA create residual unsecured exposure, and how is this quantified?

The threshold (H) and minimum transfer amount (MTA) in a CSA create a gap between the actual derivative exposure and the collateral held. This gap represents residual unsecured exposure — the amount at risk if the counterparty defaults at the worst possible moment within the CSA parameters.\n\nMaximum Unsecured Exposure:\n\nThe worst-case unsecured exposure under a CSA is:\n\nMax Unsecured Exposure = H + MTA + Potential market move during MPOR\n\nThis is because:\n- The exposure can reach the threshold before any collateral is required\n- The MTA means even when the threshold is breached, small excesses are not called\n- During the MPOR, the exposure can move further without being collateralized\n\nStep-by-Step Breakdown:\n\n| Component | Source of Residual Exposure |\n|---|---|\n| Threshold (H) | Contractual permission to remain unsecured up to H |\n| MTA | Operational minimum — calls below MTA are not made |\n| MPOR move | Market movement between last clean call and close-out |\n| Settlement lag | 1-2 day delay in receiving called collateral |\n\nWorked Example:\nFairpoint Securities has a CSA with Northgate Investments:\n- Threshold (H) = $8 million\n- MTA = $750,000\n- MPOR = 10 business days\n- Portfolio volatility (10-day, 97.5%) = $3.4 million\n\nMaximum residual unsecured exposure:\n= $8M + $0.75M + $3.4M = $12.15 million\n\nEven though both parties agreed to exchange collateral, Fairpoint could face a $12.15 million loss if Northgate defaults at the worst moment. Compare this to a zero-threshold CSA:\n= $0 + $0.75M + $3.4M = $4.15 million\n\nReducing the threshold from $8 million to zero cuts the maximum unsecured exposure by 66%.\n\n`mermaid\ngraph TD\n A[\"Portfolio MTM = $0\"] --> B[\"MTM rises to $8M
Still below threshold
No collateral posted\"]\n B --> C[\"MTM rises to $8.6M
Excess = $0.6M < MTA ($0.75M)
Still no margin call\"]\n C --> D[\"MTM rises to $9.2M
Excess = $1.2M > MTA
Margin call issued for $1.2M\"]\n D --> E[\"During MPOR:
MTM could rise $3.4M more
before close-out\"]\n E --> F[\"Worst-case unsecured:
$8M + $0.75M + $3.4M
= $12.15M\"]\n`\n\nImpact on CVA:\n\nThe expected exposure profile under a CSA with non-zero threshold is modeled as:\n\nEE_CSA(t) = E[max(V(t) - C(t), 0)]\n\nwhere C(t) is the collateral held at time t. The collateral is bounded by:\n\nC(t) = max(V(t - delta) - H - MTA, 0) for V(t - delta) > H + MTA\n\nHere delta represents the MPOR. The CVA under this CSA:\n\nCVA_CSA = integral of DF(t) x EE_CSA(t) x PD(t) x LGD dt\n\nis substantially lower than uncollateralized CVA but strictly greater than zero due to the threshold, MTA, and MPOR contributions.\n\nPractice CVA calculations with CSA parameters in our FRM Part II question bank.