The document discusses initial margin requirements for cleared interest rate swaps. It explains that initial margin is a portfolio measure required by central clearinghouses and is calculated using Value-at-Risk models based on historical simulation. The Value-at-Risk indicates the potential loss of a portfolio over a given time period at a certain confidence level, and is used to determine the initial margin amount required by the clearinghouse.

1. CCP Initial Margin for Interest
Rate Swaps
Amir Khwaja
Partner, Clarusft Consulting LLP
September 19, 2012

2. Agenda
Margining of Bi-lateral and Cleared Trades
Initial Margin
VaR - Historical Simulation
VaR – New Trades
VaR - Advanced
Summary
September 19, 2012

3. Margining of Bi-lateral and Cleared Trades
Bi-lateral Interest Rate Swap under ISDA CSA
− Independent Amount
− Variation Margin
Cleared Interest Rate Swap
− Initial Margin
− Variation margin
Independent amount is
− usually not exchanged,
− or it is only required for certain trades (e.g. structured derivatives),
− or it is a portfolio measure based on VaR or Stress Scenarios
Initial margin is always required and is a portfolio measure
September 19, 2012

4. Initial Margin
What is the purpose?
In the event of default, use members margin funds to cover loss
Clearing House resources in event of a member default
− Margin funds of defaulting member
− Collateral from Clearing House Default fund
− Other Collateral posted by Defaulting member
− Member assessments to replenish the Default Fund
− Clearing House backstop facilities
− Clearing House Capital
Portfolio is exposed to market risk loss in the time it takes to hedge
and close-out the defaulting members portfolio
Members margins should be sufficient for this
− Variation margin is the daily P&L for the account
− Initial Margin is the amount required by the Clearing House to hold the position
September 19, 2012

5. Value-at-Risk
Value-at-Risk (VaR) is the most common method used
− LCH, CME, SGX, Eurex
It is a measure familiar to banks for monitoring market risk
Is required under Basel II and Basel III in determining the market
risk capital requirement of banks
So if an account has a VaR of $37 million
− We need to know the confidence level e.g. 99%
− And the holding period e.g. 5 days
− And can then say this means that the account could make or lose more than
$37m in a 5 day period, in average on only 1 out of 100 days
− Note it does not say whether it could make or lose $37m or $370m!
As Margin is the first-line of defence, it is reasonable to use VaR
− Default Fund & Clearing House facilities are used to cover the rest
September 19, 2012

6. VaR - Historical Simulation
Historical Simulation is the most common method to calculate VaR
− LCH, CME, SGX, Eurex
It is the most easily understood of the methods
− Variance-Covariance
− Monte-Carlo Simulation
As has less modelling assumptions than above two (e.g. Normal Dist)
It relies on choosing:
− A historical period, e.g. 4Y
− A holding period e.g. 5 days
− Generating daily holding period returns in this period e.g. daily 5d overlapping
− Calculating the P&L impact on a portfolio by applying these returns to today
− Ordering the P&L outcomes by decreasing loss
− Interpolating for the desired confidence level or probability e.g. 99%
September 19, 2012

7. VaR - Historical Simulation
USD 5Y Swap Rate
5d returns (bps)
Sep08 to Sep12
80.00
60.00
40.00
13Dec10 > 20bps
20.00
0.00
-20.00
-40.00
-60.00 20Nov08 > -60bps
-80.00
September 19, 2012

8. VaR - Historical Simulation
Assume our portfolio has a PV01 (PVBP, DV01) of $1million
− Assume for simplicity that USD 5Y Swap is the only market factor for the portfolio
− (In reality there are many market risk factors for USD and other Currencies)
− For a 1 bps rise in the 5Y Swap rate, our Profit will be $1m
− For a 1 bps fall in the 5Y Swap rate, our Loss will be $1m
− We can calculate the PL Series for our portfolio by multiplying the bps returns on
each day by $1 million, which is shown below
Profit Loss
Sep08 to Sep12
80.00
60.00
40.00
20.00
0.00
-20.00
-40.00
20Nov08 > $60m
-60.00
-80.00
September 19, 2012

9. VaR - Historical Simulation
This PL Series
− Has a PL value for each business day from 5 Sep 08 to 4 Sep 12
− A total count of 1043 values
− Each of which corresponds to a specific scenario date, starting on 5 Sep 08
− And the first element represents the PL outcome of applying the 5-day return
shift between 1 Sep 08 and 5 Sep 08 to todays market data and todays portfolio
We call this the PL vector of the portfolio
− The first few elements of which are shown below
-26.51 09/05/2008
-5.97 09/08/2008
-12.75 09/09/2008
-6.47 For these dates 09/10/2008
-3.29 09/11/2008
-15.83 09/12/2008
-14.76 09/15/2008
-37.08 09/16/2008
-9.98 09/17/2008
-16.55 09/18/2008
22.76 09/19/2008
71.55 09/22/2008
September 19, 2012

10. VaR - Historical Simulation
The PL vector can then be re-ordered by decreasing loss
− Keeping a note of the scenario date and PL of each
− The first part of this is shown below
1 -62.58 11/20/2008
2 -56.16 12/17/2008
3 -47.79 10/21/2008
4 -46.24 10/22/2008
Re-order by PL For these dates
5 -44.95 11/21/2008
6 -42.47 06/17/2009
7 -41.29 08/14/2009
8 -39.73 12/18/2008
9 -39.62 10/06/2008
10 -37.45 10/07/2008 VaR Date
11 -37.08 09/16/2008
Now we can determine the VaR
− Which we will define as the loss of the 11th worst PL
− (We could define as 10th worst or interpolate between 10th and 11th)
− So VaR is $37.08m
− Occurs on the scenario date of 16-Sep-08, we call this the VaR Date
− This is the week of Lehman’s bankruptcy filing
September 19, 2012

11. VaR - Historical Simulation
A Histogram is a good way to view the PL vector
− Allocate each PL to a bin range
− Frequency is high for small PLs, giving the distribution below
250
Mean -1.21
Standard Deviation 13.03
Kurtosis 2.63
200 5d PLs Skewness 0.17
Sep08 to Sep12 Range 134.13
Minimum -62.58
Maximum 71.55
VaR 99% -37.08
150
Frequency
Count 1043
100
50
0
-70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
September 19, 2012

12. VaR - Historical Simulation
Zooming in to the largest losses
11th largest loss
Mean -1.21
Standard Deviation 13.03
Kurtosis 2.63
Skewness 0.17
Largest loss
Range 134.13
Expected Shortfall Minimum -62.58
Maximum 71.55
VaR 99% -37.08
Count 1043
September 19, 2012

13. VaR – Historical Simulation
An account has an Initial margin as determined by the CCP
VaR is a non-additive measure
− So we cannot calculate the VaR of a new trade
− And add to the VaR of the acount
− To estimate the new VaR / Initial Margin of the account
Adding a new trade to the account can:
− Make no change to the VaR
− Make a small increase in the VaR
− Make a small decrease in the VaR
− Make a large increase in the VaR
− Make a large decrease in the VaR
Let us explore why
September 19, 2012

14. VaR – New Trades
VaR is determined by a specific scenario loss
− So for our 4Y period, there are @ 260 x 4 or actually 1,043 observations
− For 99%, we assume the 11th largest loss determines the VaR
− This scenario date, is known as the VaR Date
− For our sample portfolio the VaR is $37m
− Resulting from the USD 5Y Swap Rate dropping 37 bps
September 19, 2012

15. VaR – New Trades
If the new trade is not sensitive to the USD 5Y Swap Rate
− For instance if it is a JPY 1Y Swap
− It may mean the Loss on VaR date will not change at all
− As even though there are scenarios for JPY 1Y Swap
− On the VaR Date the scenario value may be 0 (entirely plausible)
− So the VaR PL will not change
− And VaR will remain as $37m
September 19, 2012

16. VaR – New Trades
It is more likely that this trade will cause a small change
− As the JPY 1Y is more likely to have a non-zero shift on a large USD shift day
− This means that all the tail scenarios (1-11) will change slightly
− Either increasing loss (shift left) or decreasing loss (shift right)
− So the 11th loss scenario may move left or right from its value of -37.08
− Below it is shown increasing to a VaR of $37.75m
-62.58 -63.24
-56.16 -57.31
-47.79 -48.55
-46.24 -46.44
Small Changes
-44.95 -45.15
-42.47 -42.83
-41.29 -41.55
-39.73 -40.10
-39.62 -40.01
-37.45 -38.35
-37.08 -37.75
September 19, 2012

17. VaR – New Trades
If the new trade is sensitive to the USD 7Y Swap Rate
− For instance if it is a USD 7Y Swap
− As USD 5Y and 7Y rates are highly correlated, would expect that a move of -37
bps in the 5Y would have a similar direction and size move for the 7Y
− It will make a large change on the loss on the VaR Date
− It is likely to change many of the surrounding tail scenarios
− So much so that the VaR Date will change to a different one
− This is likely to mean a much larger change in VaR, either higher or lower
− Depending on whether the trade is risk reducing or risk increasing
11/20/2008 -62.58 11/20/2008 -66.24
12/17/2008 -56.16 12/17/2008 -59.31
10/21/2008 -47.79 10/22/2008 -52.55
10/22/2008 -46.24 10/21/2008 -49.44
11/21/2008 -44.95
Large Changes
11/21/2008 -48.15
06/17/2009 -42.47 06/17/2009 -46.83 New VaR Date
08/14/2009 -41.29 08/14/2009 -45.55
12/18/2008 -39.73 12/18/2008 -43.10
10/06/2008 -39.62 10/06/2008 -42.66
10/07/2008 -37.45 09/16/2008 -41.62
09/16/2008 -37.08 12/19/2008 -39.55
September 19, 2012

18. VaR – Market prices
VaR changes even when no new trades in the portfolio
Small effect
− Each PL in the tail will change by a small amount due to different market prices
− As each Swap will have a slightly different mtm value
Large effect
− If market prices differences are large enough
− Change in order of tail scenarios, so a new VaR Date (11th scenario)
11/20/2008 -62.58 11/20/2008 -66.24
12/17/2008 -56.16 12/17/2008 -59.31
10/21/2008 -47.79 10/22/2008 -52.55
10/22/2008 -46.24 10/21/2008 -49.44
11/21/2008 -44.95
Large Changes
11/21/2008 -48.15
06/17/2009 -42.47 06/17/2009 -46.83 New VaR Date
08/14/2009 -41.29 08/14/2009 -45.55
12/18/2008 -39.73 12/18/2008 -43.10
10/06/2008 -39.62 10/06/2008 -42.66
10/07/2008 -37.45 09/16/2008 -41.62
09/16/2008 -37.08 12/19/2008 -39.55
September 19, 2012

19. VaR – Scenario roll-off
VaR changes even when market data does not change
Sometimes by a very large amount
Caused by old scenarios rolling out of the historical window
− For example the Sep/Oct 2008 will no longer be in our 4Y historical period
− This is likely to mean a large change (decrease) in VaR
11/20/2008 -62.58
12/17/2008 -56.16
10/21/2008 -47.79
10/22/2008 -46.24
• Five Tail Scenarios are in Sep/Oct 2008
11/21/2008 -44.95 • These will drop off
06/17/2009 -42.47 • New scenarios in 2012 will have smaller PLs
08/14/2009 -41.29
• Other lower loss scenarios will replace these five
12/18/2008 -39.73
10/06/2008 -39.62 • The VaR will decrease substantially
10/07/2008 -37.45
09/16/2008 -37.08
September 19, 2012

20. VaR – Day to Day Changes
Adding a new trade to the account can:
− Make no change to the VaR
− Make a small increase in the VaR
− Make a small decrease in the VaR
− Make a large increase in the VaR
− Make a large decrease in the VaR
Even with no new trades VaR can change
− By a small amount
− By a large amount
This can seem non-intuitive
Unless we learn to consider the PL Vectors and Histogram
September 19, 2012

21. VaR – Advanced
Exponential weighting
− Rather than give equal weight to each of the scenatios
− Give more weight to recent observation dates over older dates
− On the intuition that recent history is a better guideline to the near future
− A more responsive VaR
− So if recent history is more volatile, the VaR is more influenced more by these
scenarios and less by the earlier ones so quicker to increase
September 19, 2012

22. VaR – Advanced
Filtered Histsim (FHS) or Volatility Scaling
− Uses current volatility to influence returns
− On the intuition that in time-series data volatility is clustered i.e. there are longer
periods of small market moves, punctuated by shorter periods of very high
market moves
USD 5Y Swap Rate
Sep08 to Sep12
80.00
60.00
40.00
20.00
0.00
-20.00
-40.00
-60.00
-80.00
September 19, 2012

23. VaR – Advanced
Filtered Histsim (FHS) or Volatility Scaling
− Uses current volatility to influence returns
− On the intuition that in time-series data volatility is clustered i.e. there are longer
periods of small market moves, punctuated by shorter periods of very high
market moves
− So VaR should be increased in the volatile periods and decreased in the stable
periods
− We need to include this volatility dynamics
− Otherwise will generate a higher or lower number of exceptions than our 99%
− FHS worked well in the Swap market in the lead up, during and post the 2007-
2008 Financial Crises
− So Initial Margin increasing faster at start of Crisis and then decreasing faster
as Crisis period ended
− Exactly the behaviour that a Clearing House and Clearing members would want
from the margins to ensure they were adequate (not too high or too low)
September 19, 2012

24. VaR – Advanced
Liquidity Adjustment
− Exit cost of a position
− Large position size in a currency or tenor
− Need to know average daily trading volume for this currency & tenor
− Need the bid/ask spread for this currency & tenor
− A position that will take longer than our holding period (5d) to sell will incur a
larger loss in bid/ask spread and longer time to sell
− So the VaR should be increased with a Liquidity adjustment factor
Credit Risk Multiplier
− Clearing House or Clearing Member may impose this
− As a multiplier on the VaR (e.g. 1.5 times)
September 19, 2012

25. VaR – Advanced
Initial Margin requirements can be high for a derivatives portfolio
− If large positions or long term or volatile markets
− Collateral needs to be posted to cover this
− It is important to understand the dynamics of Initial Margin (VaR)
The previous slides give you an intuitive feel
How do you get more detail?
− Ask the Clearing House (CCP) or Clearing Member (CM) for the risk margin
methodology documentation
− Send them a portfolio and ask for margin reports
− Good for back-loading exercises
− Good for comparison with other CCPs
− Some CCPs make software available to estimate the margin
Either Excel workbooks
Or Web Applications
− Software vendors have also recently announced offerings
September 19, 2012

26. Summary
Independent Amount is not usually exchanged in a bi-lateral Swap
Initial Margin is always required for a cleared Swap
It is a significant amount at the portfolio account level
Historical Simulation VaR is the method used by CCPs
− While there are differences in details e.g. Historical period, Confidence level
− Generally all CCP’s Initial Margin amounts are similar for equivalent portfolios
Initial Margin changes in a non-intuitive manner
We need to think about
− PL vectors and Histograms
− Scenario Dates, PLs, VaR Date
− Risk Reducing and Risk Increasing trades
− Impact of changing PLs in the tail scenarios
My contact details for questions: amir@clarusft.com
September 19, 2012