As a hypothetical example, a bank has an interest rate swap with a company, with a notional amount of 20 billion yen, in which it receives a fixed rate of 1.5% and pays a floating rate. The trade has 3 years left, and the market fixed rate for a 3-year swap is 1.0%. Assume the floating payments are the same in a replacement trade, and ignore discounting. If the company fails, what is the bank's replacement cost?
Quiz: Exposure
Last reviewed: September 26, 2026
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6 questions to check your understanding of the chapter “Exposure”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: C
The bank's replacement cost is 300 million yen. Replacement cost is the amount it costs to enter into the same trade again at current market rates. In the original trade the bank received a fixed rate of 1.5%, but a replacement trade pays only the current market rate of 1.0%. The 0.5 percentage point difference on a notional amount of 20 billion yen is 100 million yen a year. Over the remaining 3 years, that is 100 million yen × 3 = 300 million yen.
100 million yen counts only one year of the difference. 0 yen is the replacement cost for the side whose market value is negative. At this market rate, the market value to the company is negative, so if the bank failed, the company could replace the trade on better terms. For that reason, the company's replacement cost if the bank fails is zero.
Suppose instead that the market moves the other way and the 3-year fixed rate rises to 2.0%. The market value to the company then becomes positive. If the bank fails, the company's replacement cost is (2.0% − 1.5%) × 20 billion yen × 3 years = 300 million yen. The bank's replacement cost if the company fails becomes zero.
Learn more: What Is Counterparty Credit Risk?
Question 2
As a hypothetical example, the market value of a trade six months from now is simulated on 10 paths. The values on the paths are −500, −300, −200, −100, 0, 100, 200, 300, 500, and 800 million yen. What is the expected exposure (EE) at that date?
Answer and explanation
Answer: A
EE is 190 million yen. The exposure on each path is the positive part of the market value, and it is zero when the value is negative. The exposures add up to 100 + 200 + 300 + 500 + 800 = 1,900 million yen. EE is this total divided by the number of paths: 1,900 ÷ 10 = 190 million yen.
80 million yen is the average of the market values themselves. The values add up to −1,100 + 1,900 = 800 million yen, and 800 ÷ 10 = 80 million yen. Because negative values are set to zero before averaging, EE is at least as large as the positive part of the average value. 380 million yen is the average over only the 5 paths with a positive value (1,900 ÷ 5). EE is averaged over all paths, including those where exposure is zero.
Learn more: Exposure Measures: CE, PFE, EE/EPE and EAD
Question 3
A bank manages how much exposure it can accept to one counterparty with a credit limit for each counterparty. Which measure is mainly compared with the credit limit?
Answer and explanation
Answer: D
The measure compared with the credit limit is potential future exposure (PFE). PFE is a high percentile (such as 95% or 99%) of the distribution of exposure at a future date, and it describes the tail of that distribution. Deciding how large an exposure to one counterparty can be tolerated (risk tolerance) means looking at this tail. Credit limits are managed by checking at least daily that PFE is within the limit.
EE is the average exposure at a future date. It is multiplied by the probability of default to estimate expected loss, so it is used to calculate CVA. Expected positive exposure (EPE) is EE averaged over a period, and it serves as an average amount in credit risk models that combine many counterparties. Current exposure (CE) is the positive part of today's market value, and it is used to track the amount at risk today. It does not show how large exposure could become at a future date. Regulatory capital uses exposure at default (EAD), calculated by methods set by regulation.
Learn more: Exposure Measures: CE, PFE, EE/EPE and EAD
Question 4
Assume the option premium is paid at the start of the trade. Which of the following parties has no exposure to the other party after the trade starts, however the market moves?
Answer and explanation
Answer: B
The party with no exposure is the seller of an option. Once the seller has received the premium, it has nothing left to receive from the other party.
After paying the premium, the option buyer simply holds the right. The market value to the buyer does not turn negative even if it falls as the market moves, so the buyer has exposure to the seller as long as the option has value. The protection buyer in a credit default swap (CDS) receives a payment from the seller if a credit event occurs for the reference entity, so it has exposure to the seller. A party with a long FX forward has exposure to the other party if the dollar rises above the contracted rate and the market value turns positive. Because there are no payments along the way and the full amounts are exchanged at maturity, that exposure grows toward maturity.
Learn more: Exposure Profiles by Product
Question 5
An interest rate swap has a market value of zero when it is entered into. Consider the future exposure that the fixed-rate payer and the fixed-rate receiver each have to the other party. When the yield curve slopes upward, which side has the larger exposure?
Answer and explanation
Answer: A
The fixed-rate payer has the larger exposure. The fixed-rate payer gains a positive market value when rates rise, and the fixed-rate receiver when rates fall. With an upward-sloping curve, later floating rates are expected to be higher. The fixed-rate payer receives the floating rate, so its market value tilts toward positive values and its exposure is larger.
The two sides have about the same exposure when the yield curve is flat and no rise or fall in future rates is expected. The exposures of the two sides are then roughly symmetric, and neither side's exposure is larger than the other's. With an upward-sloping curve, the fixed-rate receiver's market value tilts toward negative values, so its exposure is smaller than the fixed-rate payer's.
Learn more: Exposure Profiles by Product
Question 6
As a hypothetical example, a bank values a trade with a company, L, that matures in 1 year. Ignore discounting, and assume a loss given default (LGD) of 50%. The market is in a "normal" scenario with 90% probability and a "stress" scenario with 10% probability. The exposure is 2 billion yen in the normal scenario and 6 billion yen in the stress scenario. L's 1-year probability of default (PD) is 1.5% in the normal scenario and 6.5% in the stress scenario, and the overall PD across the scenarios is 2.0%. Including wrong-way risk, what is the CVA of this trade?
Answer and explanation
Answer: C
The CVA is 33 million yen. To include wrong-way risk, use the average exposure at the time L defaults. Summing "probability × PD in that scenario × exposure" over the scenarios gives 0.9 × 1.5% × 2 billion yen + 0.1 × 6.5% × 6 billion yen = 27 million + 39 million = 66 million yen. Dividing by the overall PD of 2.0% gives an average exposure at default of 3.3 billion yen. The CVA is 3.3 billion yen × 2.0% × 50% = 33 million yen.
24 million yen uses an average exposure based on the scenario probabilities alone, 0.9 × 2 + 0.1 × 6 = 2.4 billion yen (2.4 billion yen × 2.0% × 50%). That value treats exposure and L's default as unrelated, so it leaves out the effect of the higher PD in the stress scenario. The 66 million yen figure is the value with the 50% LGD left out. The 60 million yen figure assumes that default happens only in the stress scenario, multiplying the stress exposure of 6 billion yen by the overall PD and the LGD (6 billion yen × 2.0% × 50%). It ignores defaults in the normal scenario.
Suppose instead that the PD is 2.2% in the normal scenario and 0.2% in the stress scenario. The overall PD is still 2.0%, but the average exposure at default is 0.9 × 2.2% × 2 billion yen + 0.1 × 0.2% × 6 billion yen = 39.6 million + 1.2 million = 40.8 million yen, divided by 2.0%, or 2.04 billion yen. The CVA is then 20.4 million yen, smaller than the 24 million yen when the two are unrelated.
Learn more: Wrong-Way Risk