The Fundamental Review of the Trading Book (FRTB)

A bank that calculates market risk capital uses this regulation when it documents the range of instruments placed in the trading book¹. A bank that uses the internal models approach also uses it for the monthly report of standardized approach capital for each desk² and for the validation of desks³.

What the regulation requires

The FRTB is a complete rebuild of the capital calculation that covers the market risk of banks' trading books. It was prompted by the financial crisis that began in 2007, which showed that capital for the trading book had been insufficient under extreme market stress⁴.

The Basel Committee on Banking Supervision (BCBS) published Basel 2.5 in July 2009 as an interim response and implemented it from the end of 2011. It added stressed VaR, which uses data from a stress period, to VaR, captured default and rating migration risk (the incremental risk charge), and brought the treatment of securitizations closer to that of the banking book⁵. Because it was a stopgap, however, the framework lacked consistency and the following issues remained⁵.

The BCBS began reviewing the framework in 2009 and published the final document in January 2016 after three public consultations⁴. The subsequent history is as follows.

The rows from 2016 to 2019 are in the overview by the Financial Services Agency and the Bank of Japan⁶, and the January 2023 row is in the FSA's "Overview of the Basel framework"⁷. The FSA counts this rules text as part of the Basel III finalization, and describes it as a rebuild of the standardized approach to make it risk-sensitive, together with more precise internal model measurement and stricter approval requirements⁸. The Basel framework as a whole is covered in The Basel Framework and Derivatives.

The FRTB revised three things (the boundary between the books, the standardized approach, and the internal models approach) and also strengthened the link between the standardized approach and the internal models approach. Even banks that use the internal models approach must calculate and report standardized approach capital for each desk every month². A desk that fails the tests moves to the standardized approach⁹.

Legal basis and authority

In Japan, a Financial Services Agency notice issued under the Banking Act (FSA Notice No. 19 of 2006; the "Notice") sets out the calculation of capital ratios¹⁰. Market risk capital is set out in Chapter 9 of the Notice, and the Commissioner of the Financial Services Agency approves use of the internal models approach¹¹¹². The FSA has been implementing the Basel III finalization, which includes this rules text, in stages from the fiscal year ending March 2023⁸.

Smaller banks can calculate under the simplified approach. For a bank that maintains a trading account, the conditions include that the total of the assets and liabilities in the trading account, and the net position in the foreign exchange risk category, are each below 100 billion yen¹³.

The boundary between the trading book and the banking book is in Chapter 2 of the Notice (consolidated capital ratio under the international standard). The standalone capital ratio and the domestic standard have articles with the same content in separate chapters¹⁴. Below, the provisions on the boundary are those of the consolidated chapter under the international standard.

The provisions were checked as published on October 6, 2026 (the FSA's full text, updated on August 24, 2026).

The boundary between the trading book and the banking book

The risks of trading book instruments are within the scope of market risk capital. For banking book instruments, only foreign exchange risk and commodity risk are within the scope¹⁵. The choice of book for an instrument therefore changes the capital calculation. The FRTB clarified the boundary by building on the "trading intent" of Basel 2.5 to define "trading purpose" and by giving a list of specific instruments¹⁶.

The Notice provides that the following instruments are placed in the trading book.

The following are excluded from specified transactions:

• Unlisted shares
• Instruments planned to be used as the underlying assets of a securitization
• Real estate held directly
• Credit extended to individuals or to mid-sized and smaller enterprises
• Investments in funds (except those that meet the requirements of "Group 1")
• Derivatives and funds whose underlying is any of these
• Instruments that hedge the risks of these

Instruments that fall under none of the rows in the table go in the banking book¹⁸. A bank can place specified transaction instruments and similar instruments that it holds for a purpose other than trading in the banking book by notifying the Commissioner of the Financial Services Agency in advance. Correlation trading, net short, and underwriting instruments are not eligible for this notification¹⁸. The 2016 overview by the Financial Services Agency and the Bank of Japan says that the international standard requires supervisory approval, but the Notice's text provides for notification¹⁹.

Moves between books are generally prohibited. A move is allowed as an exception only when the bank obtains approval from directors and others, conducts an internal audit, and discloses the move, and it must also notify the Commissioner of the Financial Services Agency in advance²⁰. If a move reduces required capital, the reduction is added back to required capital²⁰. A bank must document the policies and procedures that determine the range of instruments placed in the trading book, and its internal audit unit audits this classification at least once a year¹.

For internal trades (derivative transactions between organizational units of a bank or between its books), a transfer of risk from the trading book to the banking book is not included in the measurement of market risk capital. A transfer of risk from the banking book to the trading book is recognized as a hedge only in limited cases. For credit risk and equity risk, the hedge is recognized, for example, when the trading book fully offsets the position in the internal trade with an external hedge transaction with a third party²¹.

The structure of the standardized approach

Standardized approach (SA) capital is the sum of three components: the sensitivities-based method, the default risk charge, and the residual risk add-on²².

Sensitivities-based method

Capital under the sensitivities-based method is the sum of three capital amounts: delta risk, vega risk, and curvature risk²³. Delta risk is a linear estimate of the change in value caused by a small change in a risk factor (a driver of the value of a position), and vega risk is the potential loss from the change in the value of a derivative caused by movements in implied volatility²⁴. Curvature risk is the additional potential loss, for instruments with optionality, beyond delta risk²⁴. The calculation takes the change in value when a risk factor is moved by a large amount and subtracts the change that delta would predict²⁵. Delta and vega are calculated from the sensitivity to each risk factor.

Delta applies to all instruments of a desk that uses the standardized approach, except securitizations other than CTP (non-CTP). Vega and curvature apply to instruments with optionality²⁶.

There are seven risk classes: general interest rate, credit spread (split into three categories: non-securitization, non-CTP securitization, and CTP securitization), equity, commodity, and foreign exchange²⁷. Delta and vega capital are calculated in the following order²⁸.

1. Multiply the sensitivity to each risk factor by a risk weight (RW) to get the risk-weighted sensitivity $WS_k$.
2. Aggregate the $WS_k$ within a bucket using the correlation $\rho_{kl}$ between risk factors, to get the bucket capital $K_b$.
3. Aggregate the bucket capital amounts using the correlation $\gamma_{bc}$ between buckets, to get the risk class capital.
4. Add up the risk class capital amounts.

Bucket capital and risk class capital are calculated with the following formulas. $S_b$ is the sum of the $WS_k$ in bucket b.

$$K_b = \sqrt{\max\left(0,\ \sum_k WS_k^2 + \sum_k \sum_{l \ne k} \rho_{kl}\, WS_k\, WS_l\right)}$$ $$\text{Class charge} = \sqrt{\sum_b K_b^2 + \sum_b \sum_{c \ne b} \gamma_{bc}\, S_b\, S_c}$$

The correlations are applied in three scenarios. The medium scenario uses the correlations in the Notice's tables as they are, the high correlation scenario multiplies the correlations by 1.25 (capped at 1), and the low correlation scenario replaces a correlation $\rho$ with $\max(2\rho - 100\%,\ 75\%\,\rho)$. For each scenario, delta, vega, and curvature capital are added together, and the largest amount is the capital under the sensitivities-based method²⁹.

Consider a hypothetical example in which a desk of Bank R that uses the standardized approach holds two equities in the same bucket. The desk is long 10 billion yen of stock A and short 6 billion yen of stock B. The delta sensitivity is the change in value when the share price rises 1%, divided by 0.01. For a one-to-one spot holding, it equals the amount of the position, so the sensitivities are +10 billion yen and −6 billion yen³⁰. The risk weight of 20% and the correlation of 50% between risk factors are illustrative values, not values from the Notice. Assume there are no other risks.

The risk-weighted sensitivities are 2 billion yen for stock A and −1.2 billion yen for stock B. Since $K_b^2 = 2^2 + (-1.2)^2 + 2\rho \times 2 \times (-1.2) = 5.44 - 4.8\rho$, the capital in the three scenarios is as follows.

For positions in which a long and a short offset each other, the lower the correlation, the less the offset works and the larger the capital. In this example, the capital is the largest amount, 1.908 billion yen. With only one bucket, risk class capital equals $K_b$³¹.

Deep diveChanges to the standardized approach from 2016 to 2019

The overview by the Financial Services Agency and the Bank of Japan says that the standardized approach changed in the following ways between the 2016 rules text and the 2019 finalization³².

• The risk weights for general interest rate were reduced by 30% from the 2016 rules text, and those for foreign exchange by 50%.
• In credit spread, the risk weight for high-yield and unrated sovereign bonds (bucket 9) was lowered from 3.0% to 2.0%.
• A bucket for index instruments was added, and the formula for the low correlation scenario was changed to its current form (the formula above).
• A floor was introduced into the curvature risk formula to soften steps in capital.

Default risk capital

The default risk charge covers losses from the default of an obligor, which the sensitivities-based method does not capture³³. For non-securitization instruments, the bank calculates for each exposure the jump-to-default (JTD) amount, the loss if the obligor defaults. The bank then offsets long and short positions on the same obligor, assigns the exposures to buckets, and multiplies by the risk weight for each credit risk category. Within a bucket, it subtracts from the risk-weighted amount of the long positions the risk-weighted amount of the short positions multiplied by the hedge benefit ratio, and then simply adds up the amounts for the buckets³⁴.

JTD is the product of loss given default (LGD) and the notional amount, plus the mark-to-market profit or loss (P&L). For a long position it is $\max(LGD \times \text{notional} + P\&L,\ 0)$, and for a short position it is $\min(LGD \times \text{notional} + P\&L,\ 0)$. LGD is 100% for equity instruments and non-senior debt, 75% for senior debt, and 25% for covered bonds³⁵. This JTD is for exposures with a remaining maturity of one year or more. For exposures with a remaining maturity of less than one year, the amount is multiplied by the remaining maturity expressed in years (not less than 0.25)³⁶.

The following example, again with Bank R, shows how the capital for two senior bonds is built up. The bank is long the senior bond of Company A with a notional amount of 10 billion yen and short the senior bond of Company B, a different obligor, with a notional amount of 4 billion yen. Both are valued at par ($P\&L$ is 0) and have a remaining maturity of one year or more. The two companies are in the same bucket, and the credit risk category is 8-4 (risk weight 6.0%).

The hedge benefit ratio is 7.5 ÷ (7.5 + 3) = 0.714, and the bucket capital is $0.45 - 0.714 \times 0.18 = 0.321$ billion yen³⁷. Without the short position, the capital would be 0.45 billion yen.

Residual risk add-on

The residual risk add-on is capital for risks that the sensitivities-based method and the default risk charge do not capture. It applies to instruments with complex underlying assets and to other instruments that carry residual risk. The latter include instruments whose payoff cannot be replicated by a combination of plain options. The gross notional amount is multiplied by 1.0% for the former and 0.1% for the latter. Exchange-traded instruments and centrally cleared instruments, among others, are excluded³⁸.

For an instrument with a notional amount of 10 billion yen, the capital is 0.1 billion yen (100 million yen) for the former and 0.01 billion yen (10 million yen) for the latter.

The structure of the internal models approach

The internal models approach (IMA) is a method in which a bank calculates market risk capital with its own models, and only banks approved by the Commissioner of the Financial Services Agency use it¹²³⁹. The internal models approach here is a market risk approach, separate from the "expected exposure method" (the Notice's term) for counterparty credit risk⁴⁰.

Conditions for the internal models approach

Eligibility for the internal models approach is tested at three levels.

A desk is a group of traders, among others, who carry out a clearly defined business strategy⁴⁴. The Notice requires, for each desk, a head trader (in principle one person), risk limits, reporting to the board of directors and others, a document setting out the business strategy, and a risk management report at least once a week, among other requirements⁴⁵. If a desk that uses the internal models approach fails the tests, the capital for that desk is calculated with the standardized approach.

Expected shortfall and liquidity horizons

The core of internal models approach capital is expected shortfall (ES). ES is the average of the losses expected to exceed VaR within a given probability range⁴⁶. The statistics are covered on the Expected Shortfall page. Only the structure of the regulatory calculation is covered here.

The Notice provides that ES is calculated daily for all desks that use the internal models approach together and for the portfolio of each desk. The confidence level is one-tailed 97.5%, and the base horizon is 10 days⁴⁷. Under VaR, a uniform holding period of 10 days was assumed⁴⁸. The FRTB instead uses liquidity horizons that depend on the market liquidity of each risk factor. There are five liquidity horizons (10, 20, 40, 60, and 120 days), and the Notice sets them for each category of risk factor.

A liquidity horizon is a floor rather than a fixed value, and with approval a desk can set a longer period⁴⁷⁴⁸. The liquidity horizons are reflected by combining 10-day ES figures with the following formula.

$$ES = \sqrt{\left(ES_T(P)\right)^2 + \sum_{j \ge 2}\left(ES_T(P, j)\sqrt{\frac{LH_j - LH_{j-1}}{T}}\right)^2}$$

$T$ is 10 days, $ES_T(P)$ is the 10-day ES calculated by moving all risk factors, and $ES_T(P, j)$ is the 10-day ES calculated by moving only the risk factors with a liquidity horizon of at least $LH_j$. $LH_1$ to $LH_5$ are 10, 20, 40, 60, and 120 days.

The following example continues with Bank R. Assume the ES from moving all risk factors is 10 billion yen. The ES from only the risk factors with a liquidity horizon of at least 20 days is 6 billion yen, and the ES from only those with at least 40 days is 3 billion yen. None have a horizon of 60 days or more.

The sum of squares is 154, and ES is 12.41 billion yen⁴⁹. If all liquidity horizons were 10 days, it would be 10 billion yen, so the more risk factors with low liquidity a bank holds, the larger the capital.

The capital calculation also uses data from a period of market turmoil. "Stressed ES", the ES calibrated to a stress period, is the ES calculated from the 12 months of the harshest market conditions within an observation period that goes back to at least 2007⁵⁰. The Notice calculates the capital for modellable risk factors (IMCC) from two values: the value calculated for the five risk classes together and the sum of the values calculated for each risk class. It combines them with a coefficient of 0.5⁵¹. For example, if the value for all risk classes together is 4 billion yen and the sum of the values for each risk class is 5 billion yen, IMCC is 0.5 × 4 + 0.5 × 5 = 4.5 billion yen.

Deep diveThe formula for stressed ES

Stressed ES is calculated by multiplying the ES for the stress period by a ratio based on the most recent 12 months⁵².

$$ES = ES_{R,S} \times \max\left(\frac{ES_{F,C}}{ES_{R,C}},\ 1\right)$$

$ES_{R,S}$ is the ES calculated with stress period data for the reduced set of risk factors. The reduced set is a subset of the modellable risk factors that have a sufficient observation history. Next, $ES_{R,C}$ is the ES for the same risk factors calculated with data from the most recent 12 months. Likewise, $ES_{F,C}$ is the ES for all risk factors calculated with data from the most recent 12 months. The reduced set must meet requirements such as an average of at least 75% over the most recent 12 weeks for the ratio of $ES_{R,C}$ to $ES_{F,C}$.

Non-modellable risk factors

The risk factor modellability test determines whether a risk factor may be included in the ES model. A risk factor that fails the test is a non-modellable risk factor (NMRF)⁵³. The test counts observations of real prices linked to the risk factor. The criterion is at least 24 observations in the most recent 12 months and at least 4 in every 90-day period, or at least 100 observations (in both cases at most one per day)⁵⁴. Real prices include the prices of the bank's own transactions, prices of actual transactions between third parties, and prices that refer to committed quotes, and they do not include prices referred to for exchanging collateral for margin⁵⁴.

Capital for an NMRF is calculated with a stress scenario rather than with ES. The scenario uses a one-tailed 97.5% confidence level, a common 12-month stress period for all NMRFs in the same risk class, and a liquidity horizon of at least 20 days⁵⁵. The capital for NMRFs (SES) is the sum of the following three terms.

$$SES = \sqrt{\sum_i ISES_i^2} + \sqrt{\sum_j ISES_j^2} + \sqrt{\left(\rho \sum_k SES_k\right)^2 + (1 - \rho^2)\sum_k SES_k^2}$$

$i$ indexes NMRFs for idiosyncratic credit spread risk⁵⁶. $j$ indexes NMRFs for the idiosyncratic risk of equities, and $k$ indexes all other NMRFs. $ISES_i$ and $ISES_j$ are the capital for a single NMRF each. $SES_k$ is the capital for a single NMRF $k$. $\rho$ is 0.6⁵⁵. For example, if there are two other NMRFs with capital of 3 billion yen and 4 billion yen, then $\rho \sum SES_k = 0.6 \times 7 = 4.2$ and $(1 - 0.36)(9 + 16) = 16$, so SES is $\sqrt{4.2^2 + 16} = 5.8$ billion yen. This falls between the simple sum of 7 billion yen and the 5 billion yen that results from assuming zero correlation.

Default risk and the overall aggregation

For desks that use the internal models approach, default risk capital is calculated with the DRC model. It uses default simulation to measure, every week, a credit value at risk at a one-tailed 99.9% confidence level over a one-year holding period (60 days is allowed for equity portfolios). The capital is the larger of the latest measured value and the average of the latest 12 weeks⁵⁷.

Internal models approach capital other than DRC ($C_A$) is the larger of the sum of IMCC and SES on the calculation reference date and an amount that uses the average over the most recent 60 business days⁵⁸.

$$C_A = \max\left\{IMCC_{t-1} + SES_{t-1},\ m_c \cdot IMCC_{avg} + SES_{avg}\right\}$$

$IMCC_{t-1}$ and $SES_{t-1}$ are the values on the calculation reference date. $IMCC_{avg}$ and $SES_{avg}$ are the averages over the most recent 60 business days including the reference date. $m_c$ is the sum of two parts. One is a multiplier that depends on the number of exceptions in the bank-wide backtest (1.50 for 0 to 4 exceptions and 2.00 for 10 or more). The other is a qualitative add-on that the Commissioner of the Financial Services Agency specifies⁵⁹⁵⁸.

Desk-level backtesting and P&L attribution tests

A desk that uses the internal models approach must pass both the desk-level backtest and the P&L attribution test³. Only the regulatory determination is covered here.

The desk-level backtest compares the daily VaR over the most recent 250 business days with hypothetical and actual P&L. VaR is calculated at two confidence levels, 97.5% and 99%. A desk with more than 30 exceptions at 97.5% or more than 12 at 99% over the most recent 12 months calculates capital with the standardized approach⁶⁰.

The P&L attribution test compares, for each desk and every day, the risk-theoretical P&L calculated by the desk's risk management model with the hypothetical P&L, which is the previous day's positions revalued with the day's closing market data. The metrics are the Spearman rank correlation, which looks at the rank correlation of the two P&Ls, and the test statistic of the Kolmogorov-Smirnov (KS) test, which looks at how close the distributions are. They are calculated with data from the most recent 250 business days⁶¹. The result falls into one of three zones⁶².

A red desk can use the internal models approach again only if a fresh test is green and the desk has had no desk-level backtesting exceptions in the most recent 12 months⁶².

Figure description

The figure checks, desk by desk, whether the internal models approach can be used for capital, through four questions in order, including the three-level judgment in the table of the previous section. A no to any question means the desk's capital is calculated under the standardised approach, and a yes to all means the internal models approach. Amber is on the yes side of the fourth question, with a capital surcharge added. Conditions other than these four, such as the treatment of non-modellable risk factors, are not included.

As Figure 1 shows, approval of the bank alone is not enough to use the internal models approach: the desk-level requirements and two tests follow. The capital surcharge for amber desks and the aggregation of the bank's overall capital are as follows⁵⁸.

$$ACR_{total} = \min\left\{IMA_{G,A} + \text{surcharge} + C_U,\ SA_{all}\right\} + \max\left\{0,\ IMA_{G,A} - SA_{G,A}\right\}$$ $$\text{surcharge} = k \cdot \max\left\{0,\ SA_{G,A} - IMA_{G,A}\right\}, \quad k = 0.5 \times \frac{\sum_{i \in A} SA_i}{\sum_{i \in G,A} SA_i}$$

$ACR_{total}$ is the total of capital for market risk (the "market risk equivalent amount") under the internal models approach and the standardized approach.

In this formula, $IMA_{G,A}$ is the total of ES capital ($C_A$) and default risk capital for the green and amber desks. Next, $SA_{G,A}$ is the capital for those two zones' desks calculated with the standardized approach. Likewise, $SA_{all}$ is the capital for all desks calculated with the standardized approach. Further, $C_U$ is the standardized approach capital for desks that do not use the internal models approach (such as red desks). Also, $SA_i$ is the capital for desk i calculated with the standardized approach. Finally, $A$ is the set of amber desks, and $G,A$ is the set of green and amber desks.

The following example continues with Bank R. Suppose $SA_i$ is 12 billion yen for the green desk, 8 billion yen for the amber desk, and 6 billion yen for the red desk. $SA_{G,A}$ is 20 billion yen, $SA_{all}$ is 26 billion yen, and $k$ is 0.5 × 8 ÷ 20 = 0.2.

If internal models approach capital is below standardized approach capital, the total is smaller than the 26 billion yen from calculating all desks with the standardized approach. If it is above, the excess is added and the total exceeds 26 billion yen⁶³.

Application dates in Japan and implementation in other jurisdictions

In Japan, the amendment of the Notice (FSA Notice No. 22 of 2022) has applied since March 31, 2023. Under the transitional measures, however, the capital ratio until the day on which one year (two years for domestic-standard banks that do not use internal models) has passed from the date of application is calculated under the previous rules⁶⁴. The FSA's document summarizes the resulting application dates as follows⁷. The supplementary provisions of the Notice support only the two categories of one year and two years later, and the categories in the table below are the FSA document's summary.

Figure description

The figure arranges the application dates of the Japanese notification from oldest to newest. The first application date is marked with a filled dot, and because of transitional measures most banks implement in the two later stages. Banks that wish to apply early can do so from the first date by notifying the FSA. The two later stages are split by bank category and differ by one year; the banks in each category are in the table in the text.

Banks that use the internal models approach also have a transitional measure for the P&L attribution test. Until the day on which one year has passed from the reference date, capital is calculated as if a desk classified as red or amber in the test had been classified as green⁶⁵.

The FSA's document summarizes the implementation timing in other countries and regions as of December 2025⁷.

Practical implications

In addition to the monthly report², a bank that uses the internal models approach carries out the modellability test of risk factors every quarter⁴³. The update of the range of portfolios to which the internal models approach is applied is also quarterly⁴¹.

What this article does not cover

The simplified approach calculation, the tables of risk weights and correlations, and the formula for curvature risk and its aggregation into buckets are not covered on this page. The backtesting and P&L attribution procedures, the US market risk rule (12 CFR Part 217), and capital for CVA risk and for counterparty credit risk are not covered on this page either.

Notes

1. "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" (FSA Notice No. 19 of 2006; full text updated by the FSA on August 24, 2026; in Japanese). Below, "Notice" refers to this notice and "page" to the page of the full text. Article 11-5, paragraphs 1 and 3 (page 57). ↩ ↩² ↩³

2. Notice, Article 271-2, paragraphs 2 and 3 (page 434). ↩ ↩² ↩³

3. Notice, Article 275, paragraphs 1 and 2 (page 459). ↩ ↩²

4. Financial Services Agency and Bank of Japan, "「マーケット・リスクの最低所要自己資本」の概要" (Overview of "Minimum capital requirements for market risk", our translation) (April 2016), page 2, "最終文書公表の経緯" (Background to the publication of the final document) (in Japanese). ↩ ↩²

5. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (April 2016), page 3, "バーゼル 2.5 と未解決の課題" (Basel 2.5 and unresolved issues) (in Japanese). ↩ ↩²

6. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (January 2019), page 2, "経緯" (Background). It covers the January 2016 publication, the December 2017 postponement, the March 2018 public consultation, and the January 2019 publication of the final rules text (in Japanese). ↩

7. Financial Services Agency, "バーゼル規制の概要" (Overview of the Basel framework, our translation) (August 2026), page 10, "バーゼルⅢ最終化の実施時期" (Implementation timing of the Basel III finalization). It covers the international implementation date (January 2023; originally January 2022, postponed by one year because of the COVID-19 pandemic), the application dates in Japan, and the timing and plans in other countries (as of December 2025) (in Japanese). ↩ ↩² ↩³

8. Financial Services Agency, "バーゼル規制の概要" (August 2026), page 9, "バーゼルⅢ最終化の概要" (Overview of the Basel III finalization), the market risk column, and the description of implementation in Japan (in stages from the fiscal year ending March 2023) (in Japanese). ↩ ↩²

9. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (April 2016), page 8, "標準的方式と内部モデル方式の関係" (Relationship between the standardized approach and the internal models approach), item 3 (in Japanese). ↩

10. Notice (FSA Notice No. 19 of 2006), title (page 1). ↩

11. Notice, table of contents (pages 5–6), Chapter 9. Section 8 is Article 302-9. ↩

12. Notice, Article 272 (page 440). ↩ ↩²

13. Notice, Article 271-2, paragraph 4, item 1 (pages 434–435). The Japanese term for the trading account is 特定取引勘定. ↩

14. Notice, Article 271-2, paragraph 6, item 2 (page 435), which refers to item 2(b) of paragraph 3 of Articles 11-3, 22-3, 34-3, and 45-3. The articles on the boundary in the international-standard consolidated chapter are Articles 11-2 to 11-12 (from page 55). ↩

15. Notice, Article 271, paragraph 1 (page 433). ↩

16. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (April 2016), page 4, "トレーディング勘定と銀行勘定の境界（1）" (Boundary between the trading book and the banking book (1)) (definition of purpose), and page 5, "トレーディング勘定と銀行勘定の境界（2）" (Boundary (2)) (list of instruments) (in Japanese). ↩

17. Notice (FSA Notice No. 19 of 2006), Article 11-3, paragraphs 1 to 5 (pages 55–56). ↩ ↩² ↩³ ↩⁴ ↩⁵

18. Notice, Article 11-4, paragraphs 1 and 2 (page 57). ↩ ↩²

19. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (April 2016), page 5, "トレーディング勘定と銀行勘定の境界（2）" (Boundary between the trading book and the banking book (2)) (in Japanese). ↩

20. Notice (FSA Notice No. 19 of 2006), Article 11-6, paragraphs 1 to 3, and Article 11-7, paragraph 1 (page 58), and Article 11-8, paragraph 2 (page 59). ↩ ↩² ↩³

21. Notice, Article 11-9, paragraphs 1 and 2 (page 59), and Article 11-10, paragraph 1 (page 59). ↩

22. Notice, Article 280 (page 478). ↩

23. Notice, Article 281 (page 479). ↩

24. Notice, Article 1, items 106, 107, and 108 (pages 25–26). ↩ ↩²

25. Notice, Article 282-3, paragraph 2 (pages 481–482). ↩

26. Notice, Article 282 (pages 479–480). ↩

27. Notice, Article 280-2, item 1 (pages 478–479). ↩

28. Notice, Article 282-2 (pages 480–481). The symbols in the formulas are those of the Notice, and $S_b$ is the sum of the $WS_k$ in the bucket. ↩

29. Notice, Article 282-4, paragraphs 1 to 3 (page 483). ↩

30. Notice, Article 283-3, item 3 (page 491). The formula is $s_k = (V_i(1.01\,EQ_k) - V_i(EQ_k)) / 0.01$. ↩

31. The calculation uses hypothetical values for illustration. $WS_1 = 0.2 \times 10 = 2$ and $WS_2 = 0.2 \times (-6) = -1.2$. The correlation in the high correlation scenario is $\min(1.25 \times 0.5,\ 1) = 0.625$, and in the low correlation scenario it is $\max(2 \times 0.5 - 1,\ 0.75 \times 0.5) = 0.375$. $K_b$ is rounded to the third decimal place. ↩

32. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (January 2019), page 5 (risk weights for general interest rate, credit spread, and foreign exchange), page 6 (bucket for index instruments), page 9 (low correlation scenario), and page 10 (curvature floor) (in Japanese). ↩

33. Notice (FSA Notice No. 19 of 2006), Article 288 (page 524). ↩

34. Notice, Article 289-3, paragraphs 2 to 5 (pages 528–529; the risk weight for credit risk category 8-4 is in the table on page 528). ↩

35. Notice, Article 289, items 1 to 3 (pages 525–526). ↩

36. Notice, Article 289, item 6 (page 526). ↩

37. The calculation uses hypothetical values for illustration. $HBR = 7.5 / (7.5 + 3) = 0.7143$, and $0.06 \times 7.5 - 0.7143 \times 0.06 \times 3 = 0.45 - 0.1286 = 0.3214$, rounded to the third decimal place. ↩

38. Notice (FSA Notice No. 19 of 2006), Article 292, paragraphs 2 to 7 (pages 535–537). ↩

39. Notice, Article 1, items 12-2 and 12-3 (page 10). ↩

40. Notice, Article 79, paragraph 1 (page 188). The credit equivalent amount of derivative transactions is calculated with SA-CCR or the expected exposure method. ↩

41. Notice, Article 272-6, paragraph 1, items 1 to 9 (pages 441–442). ↩ ↩²

42. Notice, Article 271-4, paragraph 1 (page 438), Article 271-6, paragraph 1 (page 438), and Article 275, paragraph 2 (page 459). ↩ ↩²

43. Notice, Article 274-5, paragraph 1 (page 456). ↩ ↩²

44. Notice, Article 1, item 89 (page 24). ↩

45. Notice, Article 271-3, paragraph 3, items 1, 2, 4, 5, 8, and 10 (pages 435–437). ↩

46. Notice, Article 1, item 96 (page 25). ↩

47. Notice, Article 276-2, paragraphs 1 to 3 (pages 467–470; the table of liquidity horizons is on pages 468–469). ↩ ↩²

48. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (April 2016), page 14, "主な定量的要件" (Main quantitative requirements). It covers the holding period under the current rules, and the use of liquidity horizons as floor values that desks may lengthen with supervisory approval (in Japanese). ↩ ↩²

49. The calculation uses hypothetical values for illustration. $\sqrt{10^2 + (6 \times 1)^2 + (3 \times \sqrt{2})^2} = \sqrt{154} = 12.41$ (rounded to the second decimal place). ↩

50. Notice (FSA Notice No. 19 of 2006), Article 1, item 97 (page 25). ↩

51. Notice, Article 276-4 (pages 471–472). The formula is $IMCC = \rho\, IMCC(C) + (1 - \rho) \sum_i IMCC(C_i)$ with $\rho = 0.5$. ↩

52. Notice, Article 276-3, paragraph 1 and paragraph 2, item 1 (pages 470–471). ↩

53. Notice, Article 1, items 101, 104, and 105 (page 25). ↩

54. Notice, Article 274-2, paragraphs 2, 3, and 5 (pages 450–452). ↩ ↩² ↩³

55. Notice, Article 276-5, paragraphs 1 to 4 (pages 472–473). ↩ ↩²

56. Financial Services Agency and Bank of Japan, overview of "Minimum capital requirements for market risk" (January 2019), page 24, "IMA：2016 年の規則文書から最終化にかけての変更点（2）NMRF ⑤SES の計測方法の見直し（続）" (IMA: changes from the 2016 rules text to the finalization (2) NMRF (5) revision of the SES measurement method (continued)), the note to the formula (in Japanese), which calls these risk factors "信用スプレッド・リスクの個別リスク" (idiosyncratic credit spread risk, our translation). ↩

57. Notice (FSA Notice No. 19 of 2006), Article 277, paragraphs 1 to 3 (pages 473–474). ↩

58. Notice, Article 279 (pages 477–478). In the notation here, $IMA_{G,A}$ is the Notice's $IMA_{G,A}$ (the total of $C_A$ and DRC), $C_U$ is the Notice's $C_U$, and $\text{surcharge}$ is the Notice's "capital surcharge." ↩ ↩² ↩³

59. Notice, Article 275-2, paragraph 4, table (pages 460–461). ↩

60. Notice, Article 275-3, paragraphs 1, 2, and 4 (pages 461–462). ↩

61. Notice, Article 275-4, paragraph 1 (page 462), Article 275-7, paragraphs 1 and 2 (page 465), and Article 1, items 92 and 94 (page 24). ↩

62. Notice, Article 275-8, paragraphs 1 to 6 (pages 465–466). ↩ ↩²

63. The calculation uses hypothetical values for illustration. $SA_{G,A} = 12 + 8 = 20$, $SA_{all} = 20 + 6 = 26$, and $C_U = 6$. When $IMA_{G,A} = 15$, $\min\{15 + 1 + 6,\ 26\} = 22$. When it is 25, $\min\{25 + 0 + 6,\ 26\} = 26$, to which $25 - 20 = 5$ is added for 31. ↩

64. Notice (FSA Notice No. 19 of 2006), supplementary provisions (FSA Notice No. 22 of April 28, 2022), Article 1 (page 596) and Article 2, paragraphs 1 and 2 (pages 596–597). ↩

65. Notice, supplementary provisions (FSA Notice No. 22 of April 28, 2022), Article 22 (pages 606–607). ↩

66. Notice, Article 275-9 (pages 466–467). ↩

67. Notice, Article 283-2 (page 490). ↩

68. Notice, Article 275-6, paragraph 1 (page 464). ↩

69. Notice, Article 271-8, paragraph 1 (page 439). ↩