Exposure Measures: CE, PFE, EE/EPE and EAD

The exposure measure you use differs by task, even for the same trade: credit limit management, CVA calculation, and regulatory capital calculation each use a different one. The overall picture is covered in What Is Counterparty Credit Risk?.

What the six measures represent

Exposure is the amount you could lose if a counterparty defaulted. The market value of a derivative moves with the market, so managing counterparty credit risk means measuring today's amount and future amounts separately¹. A future amount is not a single number, so it is expressed as the mean or a high percentile of a distribution².

CE is the larger of a trade's current market value and zero³. If the counterparty's default ends the trade, the side with a positive value loses that value. The side with a negative value has nothing to lose, so its CE is zero. CE is also called replacement cost and may be reported either before or after deducting collateral⁴.

With a counterparty under a close-out netting agreement, the market values of the trades are offset against each other if the counterparty defaults. So every measure is calculated on the sum of market values within each group of trades covered by close-out netting (a netting set)⁵.

An interest rate swap entered at the par rate has a market value of zero at inception, so its CE is also zero. Even so, if rates move, its future value can become positive or negative. PFE, EE, and EPE measure how large CE could become at future dates⁴.

How the profile is calculated

EE and PFE lined up by future date form the exposure profile. The profile is found by generating many scenarios for market factors with the Monte Carlo method and valuing the trades in each scenario at future dates⁶. The steps are as follows.

1. Use random numbers to generate many paths for the future movements of market factors such as interest rates and exchange rates.
2. On each path, calculate the market value of the netting set at each future date. If there is a collateral agreement, also calculate the collateral held at that date and deduct it⁷.
3. At each date, take the positive part of the market value on each path and aggregate across paths. The mean is EE, and a high percentile is PFE.

If $V_i(t)$ is the market value of the netting set on path $i$ at time $t$, the exposure on that path, $E_i(t)$, is:

$$E_i(t) = \max\big(V_i(t),\ 0\big)$$

With $N$ paths, EE is the average of exposure across paths:

$$\text{EE}(t) = \frac{1}{N} \sum_{i=1}^{N} E_i(t)$$

PFE is the value at the position of the confidence level (such as 95% or 99%) when $E_1(t), \dots, E_N(t)$ are sorted in ascending order²⁸. Both EE and PFE are found for each date, so on a chart they are functions of time.

EPE is the time-weighted average of EE⁴. Let the future dates be $t_0 = 0 < t_1 < \dots < t_n = T$, where $T$ is the end of the averaging period (for example, the trade's maturity), and let $\Delta t_k = t_k - t_{k-1}$. Then:

$$\text{EPE} = \frac{1}{T} \sum_{k=1}^{n} \text{EE}(t_k)\, \Delta t_k$$

Effective EPE is the figure used under the regulatory internal model method (IMM; called the expected exposure method in Japan's capital adequacy notice). First, EE at each date is replaced so that it never falls below its maximum up to that date. The result is called effective EE, and effective EE at time 0 is set to CE⁹.

$$\text{Effective EE}(t_k) = \max\big(\text{Effective EE}(t_{k-1}),\ \text{EE}(t_k)\big)$$

Effective EPE is the average of effective EE over the first year. If the longest maturity among the trades in the netting set is less than one year, the average is taken up to that maturity⁹. If $t_1, \dots, t_m$ are the dates up to one year (or up to the maturity, if it is less than one year), then:

$$\text{Effective EPE} = \frac{1}{t_m} \sum_{k=1}^{m} \text{Effective EE}(t_k)\, \Delta t_k$$

Around 2017, rate models such as the one-factor Hull-White model, in which the yield curve at a future date can be written as a formula in the short rate, were also used in practice to compute interest rate swap profiles¹⁰.

Worked example: computing EE, PFE, and EPE

Consider a hypothetical example in which you find EE and PFE at six months from the market values of 10 paths. Amounts are in million yen.

Total exposure is 1,600 million yen, so EE is 1,600 ÷ 10 = 160 million yen. The average of the market values themselves is 600 ÷ 10 = 60 million yen, smaller than EE. Because paths with a negative value are set to zero before averaging, EE is at least as large as the positive part of the average market value.

With only 10 paths, the 95% position is hard to pin down, so this example uses the 90% PFE. Using linear interpolation between the sorted values, as the simulator does, you move (10 − 1) × 0.9 = 8.1 positions from the first value. That is one tenth of the way from the 9th value, 400 million yen, to the 10th, 600 million yen, so the 90% PFE is 400 + (600 − 400) × 0.1 = 420 million yen¹¹. One path in 10 has exposure above this value, and the PFE is about 2.6 times the EE of 160 million yen.

Next, the quarterly EE below gives EPE and effective EPE for the first year. Consider a hypothetical example in which the trade has a value of zero at time 0, so its CE is zero. EE at six months is the 160 million yen above.

EE falls to 140 million yen at 0.75 years, but effective EE stays at the previous maximum of 160 million yen. Each $\Delta t_k$ is 0.25 years, so EPE is 0.25 × (100 + 160 + 140 + 200) = 150 million yen. Effective EPE is 0.25 × (100 + 160 + 160 + 200) = 155 million yen, larger than EPE by the amount by which EE fell.

Figure description

The chart plots the EE and effective EE from the table above as lines, with time on the horizontal axis. EE rises from 0 at year 0 to 100 million yen at 0.25 years and 160 million yen at 0.5 years, falls to 140 million yen at 0.75 years, and then reaches 200 million yen at year 1. Effective EE keeps the maximum up to 0.75 years, so it stays flat at 160 million yen from 0.5 to 0.75 years and equals EE at every other date. Effective EE never falls below EE, and 0.75 years is the only date in the table where the two differ. The lines between the dates simply connect the values in the table with straight segments and are not values in the table.

The profile of a five-year swap

The simulator's initial values give the following profile for a five-year pay-fixed interest rate swap (trade A) with a notional amount of 10 billion yen. Rates move from a flat 1% curve, the interest rate volatility is 80bp, and there are 1,000 paths. Payments are annual, and the fixed rate is the par rate that makes the value zero at time 0¹².

EE peaks at 136 million yen at 1.75 years, drops to 118 million yen just after the payment at two years, and reaches zero at maturity at five years. EE grows as rates have more time to move, and falls as each payment reduces the remaining cash flows. So swap exposure forms a hump partway through the term and changes in steps around the payment dates¹³.

EPE (the average of EE up to maturity) is 96 million yen, and effective EPE (over the first year) is 73 million yen. The 95% PFE reaches its maximum of 539 million yen at 2.75 years, about four times the EE at that date (133 million yen). CE is zero just after the trade is entered, but at 2.75 years, one path in 20 has exposure above 539 million yen. At a 99% confidence level, the maximum PFE is 775 million yen¹².

If you halve the rate volatility to 40bp, EPE becomes 47 million yen, and if you double it to 160bp, EPE becomes 195 million yen, so EPE is roughly proportional to volatility. With a 10-year term, EPE is 236 million yen, and with a three-year term, it is 42 million yen¹².

Choosing a measure

Even when the measures come from the same simulation, which one you use depends on the task. To decide how large an exposure to one counterparty can be, you use PFE, which describes the tail of the distribution. For the expected loss, you use EE¹⁴.

Consider a hypothetical example in which Company F sets the limit on its exposure to one counterparty at 400 million yen, measured by the 90% PFE. The earlier 10-path example looks at only one date, six months out, where the PFE is 420 million yen, which is 20 million yen above the limit. For the same trade, the EE used in a CVA calculation is 160 million yen, a different size from the PFE. If the limit were 500 million yen, the PFE of 420 million yen would fall within it, leaving 80 million yen of room. Depending on the measure used, the same trade looks different in size.

Credit limits are managed by checking at least daily that PFE is within the limit¹⁴. How limits are set and how usage is measured, including limits on measures other than PFE (such as CVA) and comparisons with exposure under stress, is covered in Credit Limit Management.

CVA is calculated, for each future period, by discounting EE to today, multiplying by the probability that the counterparty defaults in that period and by the loss given default, and adding up the results¹⁵. The EE in the simulator is not discounted, so it must be discounted before it is used for CVA.

Values reflected in market prices, such as CVA, are valued under the risk-neutral probability. Around 2017, however, PFE for credit limits was often calculated in practice under real-world probabilities estimated from historical data, which had the advantage that limit figures did not change often¹⁶. For the same trade, PFE and EE differ depending on which probability is used.

EAD is the amount of exposure at default¹⁷. Under Japan's capital adequacy notice, EAD for derivatives is calculated as the "credit equivalent amount," using SA-CCR (the standardized approach for counterparty credit risk) or the IMM. Banks subject to the domestic standard can also use the current exposure method (CEM) if they meet certain conditions¹⁸. The IMM is available to banks approved by the Commissioner of the Financial Services Agency, and it sets the credit equivalent amount as effective EPE multiplied by a regulatory factor⁹. The SA-CCR formula also has a term called PFE. It is calculated by formula from an add-on determined by the notional amount, the remaining maturity, and other factors, and it is different from a percentile taken from a simulation¹⁹.

Assumptions and limitations

PFE is a percentile, so it says nothing about how large exposure can get beyond that point. In the explanatory material that the Financial Services Agency and the Bank of Japan published on the Basel Committee on Banking Supervision's guidelines, the two authorities list two practices: using other methods, such as stress testing, to cover risks that PFE does not capture, and checking PFE through backtesting²³.

The profile depends on the model for market factors and on the assumed size of their movements (volatility). If markets move more than assumed, actual exposure will differ from the model's EE. To obtain IMM approval, a bank must have a control unit independent of the trading units. It must also use stress testing to analyze the gap between actual exposure and EE when markets move beyond the model's assumptions, and regularly check the model's accuracy through backtesting and other means²⁴.

EE is calculated from scenarios for market factors alone, separately from how likely the counterparty is to default. The relationship in which a counterparty's probability of default and the exposure to it rise together is called wrong-way risk²⁵. With wrong-way risk, exposure in the situations where default occurs is larger than EE. For this reason, banks using the IMM also put in place a framework to identify and manage wrong-way risk²⁶.

Notes

1. Office of the Comptroller of the Currency et al., "Interagency Supervisory Guidance on Counterparty Credit Risk Management" (June 2011), III.1, page 5. It calls for measuring current exposure and potential exposure separately. ↩

2. Eduardo Canabarro and Darrell Duffie, "Measuring and Marking Counterparty Risk" (Asset/Liability Management of Financial Institutions, Euromoney Books, 2003), "Counterparty exposures," "Definitions," pages 122–123. It explains that the 95% PFE, for example, is the level exceeded with only a 5% probability, and takes a high percentile of the simulated distribution. ↩ ↩²

3. Financial Services Agency, "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation; FSA Notice No. 19 of 2006, consolidated version updated on August 24, 2026), Article 79-3, paragraph 2, item 3 (pages 206–207) (in Japanese). The Notice defines it as the larger of zero and the loss, based on market value, that would arise from the counterparty's default. ↩

4. "Interagency Supervisory Guidance on Counterparty Credit Risk Management," Appendix A, "Glossary," pages 20–21, "Current Exposure," "Expected Exposure," "Expected Positive Exposure (EPE)," and "Peak Exposure." The source calls a high percentile (typically 95% or 99%) of the distribution of exposure at a future date "Peak Exposure." ↩ ↩² ↩³

5. "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation), Article 79, paragraph 7 (pages 189–190) (in Japanese). Trades under a legally effective bilateral netting agreement form one netting set together, and each other trade forms a netting set on its own. ↩

6. 前田壮一 and 長谷川達也, "ＣＶＡリスク計測の枠組みの見直し" (Revising the framework for measuring CVA risk), 金融財政事情 (February 12, 2018 issue), "実務におけるＣＶＡ管理" (CVA management in practice), page 33 (in Japanese). ↩

7. Yuichi Saito, "金融規制の複合的影響を考慮したXVA" (XVA taking into account the combined effects of financial regulations), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (April 2017), Section 3 (2), page 118 (in Japanese). ↩

8. 内田善彦, "カウンターパーティー・リスクの管理とCVAの活用" (Managing counterparty risk and using CVA) (presentation, Center for Advanced Financial Technology, Bank of Japan, June 2010), "CCR量の評価" (Measuring the amount of CCR), page 17, states that calculations of PFE use the 99th percentile or similar (in Japanese). The presentation states that it reflects the author's personal views, not the official views of the Bank of Japan. ↩

9. "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation), Article 79-3, paragraphs 1 and 2 (pages 206–207) (in Japanese). The Notice writes the effective EPE formula as the sum of effective EE multiplied by $\Delta t_k$, with the last date ($t_m$ in the text) set to one year, and does not show the division by one year. When maturity is less than one year, it takes the average weighted by $\Delta t_k$ up to that maturity. ↩ ↩² ↩³

10. Yuichi Saito, "金融規制の複合的影響を考慮したXVA," footnote 27 on page 134 (in Japanese). ↩

11. There is more than one way to define a percentile. If you do not interpolate and instead take the smallest value such that 9 of the 10 paths are at or below it, the 90% PFE is 400 million yen. ↩

12. Calculated with the simulator's (exposure-profile) calculation module, using the initial values (random seed 1) and changing only the inputs stated in the text. EE and PFE are at quarterly dates and are not discounted. EPE and effective EPE average the quarterly EE with straight lines between dates (the trapezoidal rule), so they differ slightly from the sums in the worked example's formulas. ↩ ↩² ↩³ ↩⁴

13. Yuichi Saito, "金融規制の複合的影響を考慮したXVA," the explanation of Figure 2 in Section 3 (2), pages 120–121 (in Japanese). ↩

14. "Interagency Supervisory Guidance on Counterparty Credit Risk Management," V.1, "Counterparty Limits," page 13. ↩ ↩²

15. Yuichi Saito, "金融規制の複合的影響を考慮したXVA," equation (2) in Section 2 (2), page 115 (in Japanese). ↩

16. The same paper, Section 5 (4), page 131 (in Japanese). ↩

17. "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation), Article 1, item 42 (page 17) (in Japanese). ↩

18. The same Notice, Article 79, paragraphs 1 and 2 (page 188) (in Japanese). Yuichi Saito, "金融規制の複合的影響を考慮したXVA," Section 5 (2), pages 126–127 (in Japanese), uses the term EAD for the amount calculated with the same formulas that the Notice uses for the credit equivalent amount. ↩

19. Yuichi Saito, "金融規制の複合的影響を考慮したXVA," equation (14) in Section 5 (2) a (b), pages 126–127 (in Japanese). ↩

20. Eduardo Canabarro and Darrell Duffie, "Measuring and Marking Counterparty Risk," "Simulation engine," page 125. ↩

21. "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation), Article 79-3, paragraph 3, items 1, 5, and 6 (pages 207–208) (in Japanese). The Notice also allows the use of data backed out from market prices. ↩

22. Eduardo Canabarro and Darrell Duffie, "Measuring and Marking Counterparty Risk," "Trade pricing," page 126. ↩

23. Financial Services Agency and Bank of Japan, "バーゼル銀行監督委員会「カウンターパーティ信用リスク管理に関するガイドライン」について" (On the Basel Committee on Banking Supervision's Guidelines for counterparty credit risk management) (April 2025), page 13 (in Japanese). ↩

24. "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation), Article 79-3-3, items 1 to 5 (pages 213–215) (in Japanese). ↩

25. "Interagency Supervisory Guidance on Counterparty Credit Risk Management," III.6, "Wrong-Way Risk," page 10. ↩

26. "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation), Article 79-3-3, item 13 (page 216) (in Japanese). General wrong-way risk, the risk that exposure increases because the counterparty's probability of default is positively correlated with market risk factors, is defined in Article 79-3, paragraph 5, item 2 (page 209). ↩