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.

Maximum Unsecured Exposure:

The worst-case unsecured exposure under a CSA is:

Max Unsecured Exposure = H + MTA + Potential market move during MPOR

This is because:

• The exposure can reach the threshold before any collateral is required
• The MTA means even when the threshold is breached, small excesses are not called
• During the MPOR, the exposure can move further without being collateralized

Step-by-Step Breakdown:

Component	Source of Residual Exposure
Threshold (H)	Contractual permission to remain unsecured up to H
MTA	Operational minimum — calls below MTA are not made
MPOR move	Market movement between last clean call and close-out
Settlement lag	1-2 day delay in receiving called collateral

Worked Example: Fairpoint Securities has a CSA with Northgate Investments:

• Threshold (H) = $8 million\n- MTA =$750,000
• MPOR = 10 business days
• 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: = $0 +$0.75M + $3.4M = **$4.15 million

Reducing the threshold from $8 million to zero cuts the maximum unsecured exposure by 66$0"] --> B["MTM rises to $8M<br/>Still below threshold<br/>No collateral posted\"]\n B --> C[\"MTM rises to$8.6M<br/>Excess = $0.6M < MTA ($0.75M)<br/>Still no margin call"] C --> D["MTM rises to $9.2M<br/>Excess =$1.2M > MTA<br/>Margin call issued for $1.2M\"]\n D --> E[\"During MPOR:<br/>MTM could rise$3.4M more<br/>before close-out"] E --> F["Worst-case unsecured:<br/>$8M +$0.75M + $3.4M<br/>=$12.15M"]

**Impact on CVA:**

The expected exposure profile under a CSA with non-zero threshold is modeled as:

EE_CSA(t) = E[max(V(t) - C(t), 0)]

where C(t) is the collateral held at time t. The collateral is bounded by:

C(t) = max(V(t - delta) - H - MTA, 0) for V(t - delta) > H + MTA

Here delta represents the MPOR. The CVA under this CSA:

CVA_CSA = integral of DF(t) x EE_CSA(t) x PD(t) x LGD dt

is substantially lower than uncollateralized CVA but strictly greater than zero due to the threshold, MTA, and MPOR contributions.

Practice CVA calculations with CSA parameters in our FRM Part II question bank.