Japan Securities Clearing Corporation (JSCC), a central counterparty, clears yen interest rate swaps. According to JSCC's business rules and the Handling of the business rules as of September 2026, this clearing includes cleared contracts on which variation margin is exchanged with interest. These are called Cleared Contracts (Collateral Type). If you apply the idea of discounting at the interest rate paid on collateral, which rate discounts the yen cash flows covered by this variation margin?
Quiz: Collateral and XVA
Last reviewed: September 26, 2026
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6 questions to check your understanding of the chapter “Collateral and XVA”. 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: B
The discount rate is the yen overnight rate. When cash collateral covering the full market value is exchanged continuously, future cash flows are discounted at the interest rate paid on the collateral. The side with a positive market value pays that interest on the collateral it receives and returns all of it at the end. This is the same as funding the position by borrowing at the collateral rate, so the discount rate is also the collateral rate. Under JSCC's Collateral Type, the base rate for interest on variation margin for yen cleared contracts is the weighted average of the uncollateralized overnight call rate published by the Bank of Japan (TONA). Applying the idea above, the discount rate is the yen overnight rate.
The Federal Funds Rate is the base rate JSCC uses for interest on US dollar cleared contracts. Valuing at the rate at which funds are raised applies to trades without collateral. A spread from the cross-currency swap market is added only when the currency of the cash flows differs from the currency of the collateral, which does not apply to the premise of this question.
Learn more: Collateral and Discounting
Question 2
As a hypothetical example, a bank has a trade under which it will receive a fixed amount in yen from its counterparty in 5 years, and the trade has a positive market value for the bank. Under the credit support annex (CSA), the counterparty posting the collateral can choose yen or dollar cash and can switch at any time. The discount rate with yen collateral is 1.00% a year and with dollar collateral it is 0.40 percentage points higher, both constant over the period. After the counterparty chooses the collateral currency, what annual rate discounts this trade?
Answer and explanation
Answer: C
The discount rate is 1.40%. With dollar collateral, the discount rate is the rate with yen collateral plus the yen-dollar difference (+0.40 percentage points) from the cross-currency swap market: 1.00% + 0.40% = 1.40%. The side that posts collateral has a negative market value and wants to make the absolute value of that negative value smaller, so it chooses the currency with the highest discount rate. The counterparty therefore chooses dollars at 1.40% over yen at 1.00%.
1.00% is the rate if the collateral stays in yen. A lower discount rate gives the bank a larger present value. However, the right to choose the currency belongs to the counterparty, which posts the collateral. 0.60% comes from subtracting the difference to get the dollar rate (1.00% − 0.40%) and then assuming that the currency with the lower discount rate is chosen.
When the counterparty switches to dollars, the present value seen from the bank becomes smaller than under a contract that allows only yen collateral, and the difference is a loss for the bank. Seen from the counterparty, the present value of its liability becomes smaller by the same amount. If the difference were −0.40%, the discount rate with dollars would be 0.60%, and the counterparty would choose yen at 1.00%. The present value would then be the same as with yen collateral only. This calculation holds rates constant and does not include the option value that comes from movements in the difference.
Learn more: Collateral and Discounting
Question 3
XVA is the collective name for the adjustments added to or subtracted from the value found without considering credit risk or collateral (the risk-free value). A trade has a negative value and the firm is the side that pays. The firm's creditworthiness falls, and DVA (Debt Valuation Adjustment) is recalculated with the same method. How do DVA and the value change?
Answer and explanation
Answer: A
DVA rises and the value rises. DVA reflects the chance that the firm itself defaults. When the value is negative and the firm is the side that pays, the firm would escape part of its payments if it defaulted. When creditworthiness falls, the chance of default rises and the amount escaped grows, so DVA becomes larger and raises the value. Calculated with the same method and inputs, the firm's DVA is the same size as the CVA (Credit Valuation Adjustment) on the firm seen from the counterparty, with the opposite sign.
It is CVA that is determined by the counterparty's creditworthiness: the difference between the value assuming the counterparty does not default and the value that reflects the chance of default. CVA lowers the value. MVA (Margin Valuation Adjustment) is the cost of funding the initial margin posted, and KVA (Capital Valuation Adjustment) is the cost of holding regulatory capital. Both lower the value. With each adjustment expressed as an amount of 0 or more, the adjusted value is the risk-free value − CVA + DVA − FVA − MVA − KVA. Only DVA is added, so a rise in DVA raises the value.
Learn more: Overview of XVA
Question 4
As a hypothetical example, a bank has yen interest rate swaps. The sensitivity per 1bp is +5 million yen at the 5-year tenor (a point on the maturity axis) and −3 million yen at the 10-year tenor, with none at other tenors. The risk weight is 50bp at both tenors and the correlation between them is 0.6, and neither is set by SIMM. What is the initial margin found with the SIMM steps (multiply the sensitivities by the risk weight and add them up using the correlation)?
Answer and explanation
Answer: C
The initial margin is 200 million yen. The weighted sensitivity is 50 × 5 million yen = 250 million yen for the 5-year tenor and 50 × (−3 million yen) = −150 million yen for the 10-year tenor. The correlation term is doubled because the pair with the tenors swapped is counted separately: 2 × 0.6 × 250 × (−150) = −45,000. The initial margin is million yen.
250 million yen comes from forgetting to double the correlation term, which gives . 292 million yen leaves out the correlation term, which gives the amount for a correlation of 0, . 100 million yen comes from adding the weighted sensitivities as they are (250 − 150). It equals the amount for a correlation of 1. The two tenors have a positive correlation and their weighted sensitivities have opposite signs. The weighted sensitivities at 5 and 10 years therefore partly offset each other. From the counterparty's point of view, all the sensitivities have the opposite sign, but because the signs flip together in the formula, the counterparty also gets 200 million yen.
Learn more: ISDA SIMM: The Standard Model for Initial Margin
Question 5
As a hypothetical example, the spread on a credit default swap (CDS) referencing a company is 120bp (1.2%), and the recovery rate is 40%. The hazard rate stays constant from here on, and you find it with the formula that estimates it from the CDS spread and the recovery rate (the credit triangle). What is the probability that the company defaults within 2 years?
Answer and explanation
Answer: B
The probability of default is 3.92%. The hazard rate is the CDS spread divided by the loss given default (LGD), and LGD is 1 − 40% = 60%. The hazard rate is 1.2% ÷ 0.6 = 2.0%. The probability of surviving to year 2 is . The probability of default within 2 years is 1 − 96.08% = 3.92%.
4.00% is the hazard rate multiplied by the number of years (2.0% × 2). It ignores that default can occur only among those that have survived. It therefore comes out slightly too large. 2.40% multiplies the spread by the number of years without dividing by LGD (1.2% × 2). 5.82% is the probability from dividing by the recovery rate instead of LGD (1.2% ÷ 0.4 = 3.0%), which gives .
This formula gives a default probability under the risk-neutral probability, which differs from the probability that default actually occurs. When the hazard rate differs by interval, it is found from the CDS with the shortest maturity first, so the formula serves as a rough guide.
Learn more: CVA and DVA
Question 6
MVA is a valuation adjustment that adds up, over the life of the trade, the cost of funding the initial margin that is posted. Which quantity of initial margin goes into the formula for MVA?
Answer and explanation
Answer: D
What goes into the formula is the expected initial margin at each future date. For each date, the formula multiplies the funding spread, the expected initial margin, the discount factor, and the length of the interval, and adds the results over the life of the trade. As the trade runs, the sensitivities change and so does the initial margin from year to year, so today's amount alone is not enough. For an interest rate swap, you simulate the sensitivities at each future tenor to find the future initial margin.
Holding the valuation-date amount constant ignores the shape of the profile. If the profile falls year by year, it overstates MVA. Initial margin generally cannot be reused and, unlike variation margin, earns no investment income, so an amount that assumes reuse does not enter the formula. Applying the maximum to every date also differs from using the expected value at each date.
When the funding spread narrows, MVA falls and gives a valuation gain; when it widens, MVA rises and gives a valuation loss. MVA is proportional to the spread.
Learn more: FVA and MVA