Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

Credit Risk Fundamentals › Exposure at Default

Michael BrenndoerferDecember 21, 20257 min read

Quantitative FinanceAll chapters

Part 10 of 15Risk Management and Financial Risk Controls

Chapter 54Credit Risk Fundamentals › Exposure at Default

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Exposure at Default (EAD) is the amount a borrower owes when they default. It determines the scale of potential loss; even with zero recovery, losses are limited to the exposure. For a standard term loan, EAD might seem straightforward: simply the outstanding principal plus accrued interest. However, EAD becomes more complex for revolving facilities, commitments, and derivative exposures, where the amount at risk can change significantly between now and the time of default.

EAD for Loans and CommitmentsLink Copied

For drawn loans, EAD equals the current outstanding balance, a simple and observable quantity:

\text{EAD}_{\text{drawn}} = \text{Outstanding Principal} + \text{Accrued Interest}

where:

$\text{EAD}_{\text{drawn}}$ : Exposure at Default for fully funded loans
$\text{Outstanding Principal}$ : current unpaid principal balance
$\text{Accrued Interest}$ : interest earned but not yet paid

For undrawn commitments (credit lines), you must estimate how much the borrower will draw before defaulting. This introduces behavioral uncertainty: will a distressed borrower tap their available credit lines? Historically, borrowers in distress tend to draw down available credit lines aggressively, using every available source of liquidity in an attempt to survive. This means assuming zero utilization would significantly underestimate EAD. The Credit Conversion Factor (CCF) captures this behavior by estimating what portion of unused credit lines will typically be drawn before default occurs:

\text{EAD}_{\text{commitment}} = \text{Drawn Amount} + \text{CCF} \times \text{Undrawn Amount}

where:

$\text{EAD}_{\text{commitment}}$ : Exposure at Default for a facility with undrawn capacity
$\text{Drawn Amount}$ : currently utilized portion of the credit line
$\text{CCF}$ : Credit Conversion Factor, estimating the percentage of undrawn line that will be drawn before default
$\text{Undrawn Amount}$ : available but unutilized credit limit

In[17]:

Code

def calculate_loan_ead(drawn_amount, commitment_size, ccf=0.75):
    """
    Calculate EAD for a revolving credit facility.

    Parameters:
    -----------
    drawn_amount : float
        Currently utilized amount
    commitment_size : float
        Total committed credit line
    ccf : float
        Credit conversion factor for undrawn portion

    Returns:
    --------
    float : Estimated Exposure at Default
    """
    undrawn = commitment_size - drawn_amount
    ead = drawn_amount + ccf * undrawn
    return ead


# Example: \$10M commitment with \$3M currently drawn
commitment = 10_000_000
drawn = 3_000_000
ccf_val = 0.75
ead_loan = calculate_loan_ead(drawn, commitment, ccf=ccf_val)

Out[18]:

Console

Credit Facility Details:
  Total Commitment: $10,000,000
  Currently Drawn:  $3,000,000
  Undrawn Amount:   $7,000,000

Using CCF of 75%:
  EAD = $3,000,000 + 0.75 × $7,000,000
  EAD = $8,250,000

Out[19]:

Visualization

Line chart of EAD against the drawn amount for a $10M revolving facility under 50%, 75%, and 100% CCF scenarios. All three converge to $10M at full utilization, while a dotted diagonal shows the current drawn amount without conversion. — Exposure at Default as a function of current utilization for a $10M credit facility. At low utilization, EAD is dominated by the CCF-adjusted undrawn amount. The gap between current drawn amount and EAD narrows as utilization increases.

The calculated EAD of $8.25 million reflects the likelihood that a distressed borrower will utilize remaining liquidity. This is significantly higher than the current $3 million balance, showing why credit line exposures require careful EAD estimation.

Basel regulations specify minimum CCF values depending on facility type and commitment characteristics. Unconditionally cancellable commitments (like credit cards where the issuer can reduce the limit at any time) may have lower CCFs than committed facilities where you cannot withdraw the credit line. The rationale is that if you can cancel the commitment when you detect deterioration, the borrower has less opportunity to draw before default.

EAD for DerivativesLink Copied

For derivative contracts, exposure is the potential positive value the contract could have at default, not the notional amount. As we discussed when covering forwards and swaps, a derivative has both a current mark-to-market value and future uncertainty about how that value might evolve. This makes derivative EAD more complex than loan EAD, as it depends on market movements between now and the potential default date.

The Basel framework defines two components for derivative EAD that together capture both the current exposure and the potential for that exposure to increase:

\text{EAD}_{\text{derivative}} = \text{Current Exposure} + \text{Add-on for Potential Future Exposure}

where:

$\text{EAD}_{\text{derivative}}$ : Exposure at Default for a derivative contract
$\text{Current Exposure}$ : replacement cost today (max of 0 or mark-to-market value)
$\text{Add-on for Potential Future Exposure}$ : estimate of potential increase in value over the risk horizon

The current exposure equals the positive mark-to-market value (if the counterparty owes us money). If the derivative is out of the money from our perspective, meaning we owe the counterparty, the current exposure is zero since their default would not cause us a loss on this position. The add-on captures how much that exposure could grow before we could close out the position after default. This add-on depends on the volatility of the underlying risk factor and the time remaining until the position could be replaced.

In[20]:

Code

def derivative_ead(mark_to_market, notional, asset_class, maturity_years):
    """
    Simplified derivative EAD calculation.

    Uses standardized add-on percentages similar to SA-CCR methodology.
    """
    # Current exposure (only positive values create credit risk)
    current_exposure = max(0, mark_to_market)

    # Add-on factors by asset class and maturity (simplified)
    add_on_factors = {
        "interest_rate": {1: 0.005, 5: 0.01, 10: 0.015},
        "fx": {1: 0.01, 5: 0.05, 10: 0.075},
        "equity": {1: 0.06, 5: 0.08, 10: 0.10},
        "commodity": {1: 0.10, 5: 0.12, 10: 0.15},
    }

    # Find appropriate factor (use closest maturity bucket)
    factors = add_on_factors.get(asset_class, add_on_factors["interest_rate"])
    if maturity_years <= 1:
        factor = factors[1]
    elif maturity_years <= 5:
        factor = factors[5]
    else:
        factor = factors[10]

    potential_future_exposure = notional * factor
    ead = current_exposure + potential_future_exposure

    return ead, current_exposure, potential_future_exposure


# Example: 5-year interest rate swap with \$50M notional
notional_swap = 50_000_000
mtm_swap = 1_200_000  # Currently in our favor
ead_swap, ce, pfe = derivative_ead(mtm_swap, notional_swap, "interest_rate", 5)

Out[21]:

Console

Interest Rate Swap EAD Calculation:
  Notional: $50M
  Current MTM: $1.20M (in our favor)
  Maturity: 5 years

EAD Components:
  Current Exposure:            $1.20M
  Potential Future Exposure:   $0.50M
  Total EAD:                   $1.70M

The EAD of $1.70 million is materially higher than the current $1.20 million mark-to-market value, which reflects the risk that interest rates could move further in your favor before a default occurs. This conservatism is intentional: if our counterparty defaults when they owe us the most, that's precisely when our exposure matters.

Netting agreements and collateral arrangements significantly reduce derivative EAD. When parties have multiple trades under an ISDA master agreement with netting provisions, exposure is calculated on a net basis rather than summing gross positive values. If we have ten swaps with a counterparty, some in our favor and some against us, netting allows us to offset these positions, dramatically reducing credit exposure. We'll explore counterparty credit risk and these mitigation techniques more deeply in an upcoming chapter.