To calculate Expected Positive Exposure (EPE), you simulate the future value of a counterparty’s derivative portfolio at a series of time points across at least one year, floor each simulated value at zero, average across scenarios to get Expected Exposure (EE) at each time point, apply a non-decreasing constraint to produce Effective EE, and then take the time-weighted average of those Effective EE values over the one-year horizon. The result is a single dollar figure representing the average credit risk the firm carries to that counterparty, and it feeds directly into the Exposure at Default (EAD) that drives regulatory capital.
What You Need Before You Start
Three inputs sit at the base of the calculation.
Current mark-to-market values for every derivative in the counterparty’s portfolio. These are the replacement costs at today’s prices and rates, usually pulled from internal risk systems or market data providers and reconciled against trade confirmations.
A set of future time buckets covering the remaining life of the portfolio. Near-term buckets may be daily or weekly, longer-term buckets may run to months. The buckets must cover at least the first year, because the regulatory average runs over a one-year horizon. Too few points miss short exposure spikes; too many drive up computation cost without improving accuracy.
Historical market data to calibrate the simulation. The Basel framework requires at least three years of historical data, updated quarterly or more often, to set the volatilities, correlations, and other risk parameters used to project future market factors.
Step 1: Project Future Portfolio Values
Run Monte Carlo simulations that shock interest rates, foreign exchange rates, equity prices, and the other market factors driving your portfolio. Each path produces a different future for those factors, and revaluing the portfolio under each path gives you a distribution of possible portfolio values at every time bucket. Thousands of paths are standard; the more paths, the smoother the distribution at each point.
The output of this step is, for each time bucket, a long list of simulated portfolio values — one per scenario.
Step 2: Compute Expected Exposure at Each Time Bucket
At each time bucket, convert each simulated portfolio value into an exposure by taking the greater of zero or the portfolio value. If the portfolio is underwater on a given path, the firm owes the counterparty rather than the other way around, so the credit risk on that path is zero. Only positive values carry credit risk to the firm.
Expected Exposure at that time bucket is the simple average of those floored values. If you ran 10,000 paths, add up the 10,000 exposure values at that bucket and divide by 10,000. That number is your best estimate of what the firm will be owed at that future date.
Repeat for every time bucket in the horizon. Plotted across the timeline, EE typically rises as market uncertainty grows and then falls as contracts mature and cash flows settle.
Step 3: Apply the Non-Decreasing Constraint
Regulators don’t use the raw EE profile. They require Effective Expected Exposure, which forces the curve to stay flat or rise but never dip.
The formula is straightforward. At time tk, Effective EE equals the maximum of Effective EE at tk-1 and EE at tk. For the first bucket there is no prior value, so Effective EE simply equals EE.
The reason is practical. A cluster of trades maturing at month six can cause a temporary drop in raw EE even though the remaining trades still carry meaningful risk. The non-decreasing rule prevents the capital calculation from benefiting from that temporary lull. The Basel Committee defines Effective EE as “the Expected Exposure that is constrained to be non-decreasing over time.”
Step 4: Take the Time-Weighted Average Over One Year
Effective EPE is the time-weighted average of Effective EE values across the first year. Multiply each Effective EE value by the length of the time interval it represents (Δt), sum those products across all buckets within the one-year window, and the result is Effective EPE.
Weighting matters. If Effective EE is $500,000 across a three-month window and $300,000 across the following one-month window, the $500,000 figure carries three times the weight of the $300,000 figure. Sustained periods of high exposure dominate the final number; brief spikes do not. The output is a single dollar value — the constant level of exposure that would produce the same average risk as the actual fluctuating profile.
The one-year floor is not optional. Even if every contract in the netting set matures in six months, the horizon for the Effective EPE calculation does not drop below one year in most cases. This stops firms from holding minimal capital against short-dated portfolios that get rolled continuously.
Adjusting for Netting and Collateral
The simulation in Step 1 should run on net, collateralized exposures, not on raw gross contract values. Netting and collateral change the numbers that flow into every later step.
Netting first. Under a qualifying ISDA Master Agreement, positive and negative contract values with the same counterparty collapse into a single net figure. A firm owed $2 million on one swap and owing $1.5 million on another to the same counterparty uses $500,000 as the exposure, not $2 million. To get that capital relief, the firm must conduct a legal review and keep written documentation concluding that the agreement would be found valid, binding, and enforceable in every relevant jurisdiction, including in the counterparty’s insolvency. The firm also has to monitor changes in law that could affect enforceability. An agreement that would not survive a foreign bankruptcy court does not qualify.
Collateral then reduces what remains. Credit Support Annexes typically require counterparties to post variation margin in cash or government securities to offset current mark-to-market exposure. A $1 million exposure with $800,000 of posted collateral is modeled as $200,000. Initial margin covers potential future exposure and pre-funds the losses that could accumulate between the last margin call and the close-out of a defaulted portfolio.
Margin Period of Risk Floors
When collateral is in the model, you cannot assume instant access to it after a default. The Margin Period of Risk (MPOR) is the window between the last margin exchange and the final close-out of positions. Market moves during that window hit the firm with no fresh collateral coming in. Federal regulations set minimum MPOR floors:
- Five business days for repo-style transactions with daily remargining and marking-to-market, and for client-facing derivative contracts cleared through a central counterparty.
- Ten business days for other collateralized derivative contracts with daily margin maintenance.
- Twenty business days for netting sets with more than 5,000 trades, illiquid collateral, or derivatives that cannot be easily replaced.
A longer MPOR means more time for adverse moves to accumulate inside the simulation, so EPE goes up. Crossing the 5,000-trade line doubles the MPOR and can meaningfully raise the EPE for large, complex netting sets.
From EPE to Exposure at Default
Effective EPE is not the capital number. The Exposure at Default used in the capital formulas equals alpha (α) multiplied by Effective EPE, minus any recognized credit valuation adjustment. The standard alpha is 1.4, set by the Basel Committee and codified at 12 CFR 217.132.
The 1.4 factor exists because EPE, even with the non-decreasing constraint, is still an average. It does not fully capture fat tails in the exposure distribution or the correlation between a counterparty’s default probability and the firm’s exposure to that counterparty. The roughly 40 percent uplift is the buffer for those modeling limits.
Regulators can require a higher alpha where the portfolio has concentrated counterparty risk, significant wrong-way risk, or model performance problems. A bank can also apply to use its own internally estimated alpha, but it cannot go below a 1.2 floor, and earning that lower number requires demonstrating that the internal model captures the stochastic dependency of defaults across counterparties.
When Wrong-Way Risk Changes the Math
The standard EPE calculation assumes that a counterparty’s probability of default is independent of the firm’s exposure to that counterparty. When that assumption breaks, the calculation above is not the whole story.
General wrong-way risk occurs when broad market factors push exposure and default probability up together. Interest rate derivatives with a counterparty whose creditworthiness deteriorates in a rising-rate environment is the typical case. Regulators address this through a higher alpha multiplier.
Specific wrong-way risk is a direct link between the transaction and the counterparty’s default — for example, buying credit protection from a counterparty closely tied to the reference entity. These exposures come out of the normal netting set. For single-name credit default swaps with specific wrong-way risk, Loss Given Default is set to 100 percent, and EAD equals the full expected loss assuming the underlying issuer is in liquidation, with no recovery assumption left in.