ISDA SIMM: The Standard Model for Initial Margin

Initial margin amounts are reconciled with counterparties, the model is validated by risk management, and the calculation system is run by operations staff. Each of these tasks requires understanding how SIMM works.

Two ways to calculate initial margin

Among OTC derivatives, trades that are not cleared through a central counterparty (non-centrally cleared OTC derivatives trades) require financial institutions covered by the regulation to exchange initial margin with each other.

In Japan, a notice issued by the Financial Services Agency (FSA) under Article 123 of the Cabinet Office Order on Financial Instruments Business, etc. sets out how to calculate the estimated potential loss, which is the basis for the amount of initial margin¹. The notice allows two methods: using a quantitative calculation model, or using a standardized schedule. A financial instruments business operator or similar firm that uses a model must notify the Commissioner of the Financial Services Agency in advance. Any trade for which the model cannot calculate the amount is calculated with the standardized schedule¹.

A model must also meet the following standards. The model uses a one-tailed 99% confidence interval and a holding period (the period for which the firm is assumed to keep holding the trades for the estimate) of 10 days or more. The trades are divided into five categories by the main factor that drives their market value (credit, commodities, equities, foreign exchange and interest rates, and other), and the amount is calculated for each category and then added up. Offsetting and diversification of risk can be taken into account within a category but not across categories². The historical data used in the calculation must cover a period of at least 1 year and no more than 5 years, include a period of stress and recent data, and be updated at least once a year³. For interest rate trades, the model divides interest rate maturities into six or more periods⁴.

The rules of the US Commodity Futures Trading Commission (CFTC) are built the same way. Covered firms calculate initial margin each business day, using either a model that meets the standards in the rules or the table in the rules. Unlike the notification in Japan, using a model requires the written approval of the CFTC or a registered futures association⁵.

Why an industry-wide model was created

The margin rules require initial margin to be calculated as a VaR (the amount that losses exceed with a probability of 1%) at one-tailed 99% with a holding period of 10 days or more². They do not, however, fix the details of how to calculate the VaR.

The industry body, the International Swaps and Derivatives Association (ISDA), therefore published SIMM in 2016 as an industry-wide model, so that financial institutions trading with each other can agree on the amounts they exchange⁶.

In the United States in 2016, the CFTC approved the use of SIMM by individual firms. The prudential regulators that supervise banks and the National Futures Association (NFA) approved it together with the CFTC⁷. Approval is given firm by firm, and a financial institution that uses SIMM, like one that uses any other model, must keep showing that it meets the standards in the rules⁵.

SIMM calculates initial margin from the sensitivities of the trades. The approach is the same as that of the standardized approach for market risk capital requirements set by the Basel Committee on Banking Supervision (BCBS)⁸. Compared with methods that revalue each trade under market scenarios, SIMM only needs to add up sensitivities, so the calculation is simple⁹.

Adding up sensitivities with correlations

SIMM works in three steps: find the sensitivities, multiply them by risk weights, and add them up using correlations. This section explains the simple case of an interest rate swap in one currency, where one curve is used both for discounting and for projecting future rates⁶. Using separate curves is covered in The Multi-Curve Framework.

First, for each tenor (a point on the maturity axis) used to build the curve, find the change in market value when only the rate at that tenor moves by 1bp. This is the sensitivity $s_k$ for tenor $k$. $V$ is the market value of the trade, and $r_k$ is the rate for tenor $k$.

$$s_k = V(r_k + 1\,\text{bp}) - V(r_k)$$

Next, multiply the sensitivity by the risk weight $RW_k$ to get the weighted sensitivity $WS_k$. The risk weight corresponds to the VaR of the risk factor for that tenor (here, the rate)⁶.

$$WS_k = RW_k \, s_k$$

Finally, add them up using the correlation $\rho_{kl}$ between tenors $k$ and $l$ to get the initial margin $I$⁶.

$$I = \sqrt{\sum_k WS_k^2 + \sum_k \sum_{l \neq k} \rho_{kl} \, WS_k \, WS_l}$$

If two tenors have positive correlation and their weighted sensitivities have opposite signs, the second sum is negative and the initial margin becomes smaller. In practice, SIMM groups sensitivities into buckets by type of risk. For interest rates, it first groups them into buckets by currency, and then splits each currency by tenor and curve. SIMM has two kinds of parameters: the standard deviations that express how much each risk factor moves (the basis of the risk weights above), and the correlations within and across buckets⁹.

For trades that include options, SIMM also calculates, in addition to the sensitivity above (which corresponds to delta), the sensitivity to volatility (vega). It also calculates curvature, which captures how delta changes when the price of the underlying moves⁸. Curvature is the second-order term (the part that corresponds to gamma), and SIMM approximates it from the vega sensitivities. For this reason, a set of trades with no options produces no curvature¹⁰.

Deep diveHow the square-root formula relates to the normal distribution

SIMM assumes that the moves of the risk factors jointly follow a normal distribution. The standard deviation of a sum of correlated normal variables follows from the individual standard deviations and correlations through a square-root formula. The formula above uses this relationship. A calculation that uses this relationship is called the variance-covariance method. Because it assumes a distribution, it can compute the 99% loss point directly, instead of estimating it from a simulated distribution⁹.

Worked example: two opposite interest rate swaps

Consider a hypothetical example in which Bank G and Bank H have two yen interest rate swaps. Swap A has a notional amount of 10 billion yen and 5 years to maturity, and Bank G pays the fixed rate. Swap B has a notional amount of 4 billion yen and 10 years to maturity, and Bank G receives the fixed rate. For simplicity, assume that A has sensitivity only at the 5-year tenor and B only at the 10-year tenor (in reality, the tenors in between also have sensitivity).

From Bank G's point of view, when interest rates rise, the market value of A rises and that of B falls. Assume the sensitivity per 1bp is +5 million yen for A and −4 million yen for B. Assume a risk weight of 50bp at both tenors and a correlation of 0.8 between the 5-year and 10-year tenors. The risk weight and correlation values are only for showing how the calculation works. SIMM does not set them.

The weighted sensitivity is 50 × 5 million yen = 250 million yen for the 5-year tenor and 50 × (−4 million yen) = −200 million yen for the 10-year tenor. Adding the two up gives initial margin of 150 million yen¹¹.

$$I = \sqrt{250^2 + (-200)^2 + 2 \times 0.8 \times 250 \times (-200)} = \sqrt{22{,}500} = 150$$

The double sum counts each pair with $k$ and $l$ swapped as a separate pair, so the correlation term is doubled. Changing the correlation changes the initial margin for the same set of trades as follows.

With a correlation of 0.8, adding B lowers the initial margin from 250 million yen for A alone to 150 million yen. With a correlation of 0, B does not offset the moves of A, so the initial margin rises to 320 million yen. From Bank H's point of view, all the sensitivities have the opposite sign, but because the signs flip together in the formula, Bank H also gets 150 million yen. If both banks use the same model and the same parameters, they get the same figures for both the amount Bank G collects from Bank H and the amount Bank H collects from Bank G, so each side can check the other's calculation. Note that the CFTC rules do not allow a firm to offset the initial margin it posts to a counterparty against the amount it collects from that counterparty¹².

Comparison with the standardized schedule: how offsetting works

Under the standardized schedule, you first multiply the notional amount of each trade by a ratio set by the type of trade and its remaining maturity, and add up the results¹³. This page calls this amount the gross initial margin (gross IM in the notice's formula). The ratios are as follows¹³.

The gross initial margin ignores offsetting between trades. Offsetting is reflected only through the ratio of net replacement cost to gross replacement cost (NGR). Net replacement cost is the sum of the market values of the trades (0 if negative), gross replacement cost is the sum of the market values of the trades with positive market value, and NGR is net replacement cost divided by gross replacement cost. When gross replacement cost is 0, NGR is set to 1. Initial margin is calculated with the following formula¹³.

$$\text{Initial margin} = 0.4 \times \text{Gross initial margin} + 0.6 \times \text{NGR} \times \text{Gross initial margin}$$

Because NGR takes values from 0 to 1, initial margin never falls below 40% of the gross initial margin. The standardized schedule draws on the current exposure method used for derivatives in the capital adequacy rules¹⁴. The CFTC rules set the same formula using NGR. The table of ratios is also the same, except that it sets separate ratios for cross-currency swaps¹⁵.

For Bank G's two swaps in the worked example, the gross initial margin is 10 billion yen × 2% + 4 billion yen × 4% = 360 million yen. Right after the trades are made, if the market values of both are 0, gross replacement cost is 0, so NGR is 1 and initial margin is 360 million yen. Even though A and B carry risk in opposite directions, offsetting has no effect at this point.

Suppose interest rates then move, and from Bank G's point of view the market value of A becomes +100 million yen and that of B becomes −80 million yen. Net replacement cost is 20 million yen, gross replacement cost is 100 million yen, and NGR is 0.2. Initial margin calculated from Bank G's side is 0.4 × 360 + 0.6 × 0.2 × 360 = 187.2 million yen. From Bank H's point of view, the market value of A is −100 million yen and that of B is +80 million yen. The sum of market values is negative, so net replacement cost is 0 and NGR is 0. Initial margin calculated from Bank H's side is 0.4 × 360 = 144 million yen, which differs from the amount on Bank G's side¹¹.

Under the standardized schedule, how much offsetting counts depends on the size of the market values and on which side you look from. Under SIMM, offsetting depends on the direction of the sensitivities and the correlations, and even for trades with a market value of 0, opposite sensitivities offset each other between tenors with positive correlation. The risk weights and correlations in the SIMM example above, however, are not values set by SIMM, so you cannot compare 150 million yen with 360 million yen to say which is larger. What you can compare is how offsetting works in each method.

Validating and reviewing the model

A financial instruments business operator or similar firm that uses a model sets up a model management unit independent of the units that trade. The model management unit documents the policies and procedures for running the model, and records the procedures and results of backtesting. Backtesting checks the model's accuracy by comparing the amount calculated by the model with the actual change in market value over a period equal to the holding period. The comparison may instead use the change in market value that would have occurred if the set of trades had been held fixed¹⁶. The model's accuracy is validated when it is developed and periodically after that. It is also validated when its accuracy may have been lost, for example because of a significant change to the model or a structural change in the market, and the model is revised depending on the results. The calculation process is, in principle, subject to internal audit at least once a year¹⁶.

In the FSA's public consultation on the draft margin rules, one comment asked whether a firm adopting SIMM also needs the same level of backtesting as a firm that builds its own model. The FSA answered that a financial instruments business operator or similar firm using a model must put a backtesting framework in place, and that what the framework should look like is judged case by case according to the characteristics of the model¹⁷. A firm that uses a model must notify the FSA without delay of any significant change to the matters stated in the documents attached to its notification¹⁸. As an example, the FSA gives the case where adding a new risk factor changes the estimated amount to a certain degree¹⁹.

Under the US CFTC rules, a model is reviewed at least once a year and validated independently. The validation includes comparison with calculations using other data or methods (benchmarking) and backtesting. Before making a material change to an approved model, the firm must notify the CFTC and the registered futures association 60 days in advance²⁰. As of the April 2018 paper by CFTC staff, the SIMM parameters were reviewed once a year²¹.

Assumptions and limitations

SIMM assumes that the moves of the risk factors follow a normal distribution, and it approximates changes in market value with sensitivities. A 2018 paper by CFTC staff compares SIMM with the margin models that two central counterparties use for interest rate swaps. The central counterparties' models build a loss distribution from actual past moves and take daily price moves into the distribution. The SIMM parameters, on the other hand, stayed fixed until the annual review at the time of the paper (April 2018). For this reason, the paper points out that when volatility rises across the market, SIMM initial margin may increase less than margin on cleared trades²¹.

In the same paper's comparison, the SIMM holding period (10 days) is longer than that of the central counterparties the paper compared (5 days), yet the SIMM amount was not always higher. For sets of trades spanning many currencies, the SIMM amount was relatively small compared with the central counterparties' amount, and for single-currency sets of trades it was relatively large²³.

The paper gives a separate reason for each result, but presents both as conjecture. For sets of trades spanning many currencies, it says the difference in how correlations are treated may have caused the gap. The difference here is that SIMM sets the correlation between currencies to the same fixed value for every currency pair, while the central counterparties' models use actual past moves as they are. For single-currency sets of trades, differences in correlation do not matter. The paper sees the gap for these sets of trades as coming from the standard deviations of the individual risk factors. The SIMM standard deviations represent 10 days of moves, so, all else being equal, they give a higher amount than a central counterparty's model that uses 5 days of moves. The paper's view is that the difference in holding period probably caused this gap²⁴.

For interest rate trades, SIMM adds the cost of liquidating large positions only when the net delta in a currency exceeds a threshold. As a result, a portfolio of standard products and a portfolio of exotic products with the same net delta are treated the same way. The amount calculated with SIMM is the minimum amount to exchange, and each firm may add to it in its own risk management²⁵.

Notes

1. Financial Services Agency, "金融商品取引業等に関する内閣府令第百二十三条第一項第二十一号の六イの規定に基づき、金融庁長官が定める潜在的損失等見積額を算出する方法を定める件" (Method of calculating the estimated potential loss, set by the Commissioner of the Financial Services Agency under Article 123, paragraph 1, item 21-6 (a) of the Cabinet Office Order on Financial Instruments Business, etc., our translation; FSA Notice No. 15 of 2016, March 31, 2016, in Japanese; "the notice"), the preamble and Article 1. Article 1 sets out the method under Article 123, paragraph 1, item 21-11 (a) of the Cabinet Office Order, and it applies from September 1, 2016. ↩ ↩²

2. The same notice, Article 3, paragraph 1 (one-tailed 99% and a holding period of 10 days or more; for a trade with less than 10 days to maturity, the remaining period can be treated as the holding period), paragraph 2 (the sum of the amounts calculated for each of the five categories), and paragraph 3 (offsetting, diversification, and hedging effects within a category). ↩ ↩²

3. The same notice, Article 4. It also provides that no multiplier is applied to the data on past price changes. ↩

4. The same notice, Article 5, paragraph 2. ↩

5. 17 CFR 23.154(a)(1) and (a)(2) (calculation each business day, with a model or the table), and (b)(1)(i) and (ii) (written approval of the CFTC or a registered futures association, and continuing to show that the standards are met). ↩ ↩²

6. 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), page 111 (the 2016 publication) and Section 4 (1) and (2), pages 121–123 (in Japanese). Equations (8) and (9) in the paper are for a single currency with a single curve, and the symbols are the same as the paper's. ↩ ↩² ↩³ ↩⁴

7. Michael Roberson, "Cleared and Uncleared Margin Comparison for Interest Rate Swaps" (U.S. Commodity Futures Trading Commission, Division of Clearing and Risk, April 2018), "I. Introduction," page 2. The paper notes that it gives the author's views, which do not necessarily reflect the views of the CFTC. ↩

8. 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), footnote 16 on page 122 (in Japanese). ↩ ↩²

9. Michael Roberson, "Cleared and Uncleared Margin Comparison for Interest Rate Swaps," "II. Cleared IRS Margin Models and SIMM," pages 3–4. ↩ ↩² ↩³

10. The same paper, Section III, page 6. ↩

11. Calculated from the conditions in the text. The initial margin with a correlation of 0, $\sqrt{102{,}500} = 320.16$ million yen, is rounded to the nearest million yen. ↩ ↩²

12. 17 CFR 23.154(b)(2)(viii). ↩

13. The notice, Article 9. The formula is in paragraph 1, and the ratios are in the items of paragraph 2. ↩ ↩² ↩³

14. Financial Services Agency, "コメントの概要及びコメントに対する金融庁の考え方" (Summary of comments and the FSA's views, in Japanese; March 31, 2016, the date on the web page where it is posted; "the FSA's responses"), the answer to comment No. 125, page 22. ↩

15. 17 CFR 23.154(c)(1) (the table) and (c)(2) (adjustment with NGR). The US table sets separate ratios for cross-currency swaps by remaining maturity (1%, 2%, and 4%). ↩

16. The notice, Article 6 (items 1–4 and item 6). ↩ ↩²

17. The FSA's responses, comment No. 115 and the answer to it, page 21. ↩

18. The notice, Article 8, item 2. ↩

19. The FSA's responses, the answer to comment No. 123, page 22. ↩

20. 17 CFR 23.154(b)(1)(iii) (notice 60 days in advance), (b)(4) (review at least once a year), and (b)(5)(ii) (independent validation; (B) benchmarking and (C) backtesting). ↩ ↩²

21. Michael Roberson, "Cleared and Uncleared Margin Comparison for Interest Rate Swaps," Section IV.A, page 9. ↩ ↩²

22. The FSA's responses, the answer to comment No. 126, pages 22–23. ↩

23. Michael Roberson, "Cleared and Uncleared Margin Comparison for Interest Rate Swaps," "I. Introduction," page 2 (10 days for uncleared and 5 days for cleared), and "V. Conclusion," page 13. ↩

24. The same paper, Section IV.A, page 8. ↩

25. The same paper, Section IV.B, pages 11–12. ↩