Calculating initial margin (IM)
and variation margin (VM)
Shallom Moses
Associate Director
Commodity Futures Trading Commission
(CFTC)
Disclaimer: Views expressed are my own, and not CFTC
Why do we need Initial Margin for un-cleared swaps?
• Reduction of Systemic Risk
ex: Lehman Brothers
Comparison of Lehman’s cleared and un-cleared portfolios
No loss to counterparties on cleared positions
• Promotion of Central Clearing
Price transparency
Mitigation of counterparty credit risk
Portfolio Diversification benefits
Efficient use of Liquidity
• Does Central Clearing simply transfer Systemic Risk?
Minimum amount of Initial margin
The minimum amount of IM may be determined by one of two methods:
1. A standardized look-up table similar to that outlined by the BCBS/IOSCO
final policy framework.
2. A margin model that is approved by relevant supervisory authority.
Demand on Liquidity to satisfy IM requirements:
Standardized Look-up Table: € 8 trillion
Margin Model: € 0.7 trillion
Note1: These are estimates and the actual values could differ widely based on:
• Level of offsets between positions in a portfolio
• Type of Margin Model
• Pro-cyclicality considerations
Note2: Derive liquidity demands on un-cleared swaps based on information from
cleared swaps
Methodologies for calculating initial margin (IM)
• Schedule Based Approach
• Model Based Approach
Parametric Models
Normal Model
SPAN Model
T-Copula model
Historical Models
Historical Simulation (HS)
Filtered Historical Simulation (Filtered HS)
Extreme Value Theory (EVT)
• Standard Initial Margin Model (SIMM): ISDA Proposal
Scheduled Based Approach: IM is a certain percentage of margin
Asset Class
IM (% of Notional)
Credit (0 -2 years)
2%
Credit (2 -5 years)
5%
Credit 5+ years
10%
Commodity
15%
Foreign Exchange
6%
Interest Rate (0 -2 years)
1%
Interest Rate (2 -5 years)
2%
Interest Rate 5+ years
4%
Other
15%
Standardized haircut schedule
Asset Class
Haircut
(% of Market Value)
Cash in same currency
0%
High-quality government and central bank securities: residual maturity less than one year
0.5%
High-quality government and central bank securities: residual maturity between 1 and 5 years
2%
High-quality government and central bank securities: residual maturity greater than 5 years
4%
High-quality corporate\covered bonds: residual maturity less than one year
1%
High-quality corporate\covered bonds: residual maturity between 1 and 5 years
4%
High-quality corporate\covered bonds: residual maturity greater than 5 years
8%
Equities included in major stock indices
15%
Gold
15%
Additional (additive) haircut on asset in which the currency of the derivatives obligation
differs from that of the collateral asset
8%
Net standardized initial margin = 0.4 * Gross initial margin
+ 0.6 * NGR * Gross initial margin
Where
Gross Initial Margin = Sum of individual instrument margin
NGR = Net Replacement Cost/Gross Replacement Cost for
transactions subject to legally enforceable netting arrangements
Portfolio netting or offsets are not clearly defined
Margin could be much higher
IM Based on Margin Models
Criteria
Margin Period of Risk = 10 days
Confidence level = 99%
Historical data should include period of stress
Internal governance process
Any risk offsets should be within a well defined asset class
Normal Model
Ex: Current Price = $100
1 day volatility (based on historical data) = 1%
10 day volatility = 1%*sqrt(10) = 3.16%
99th percentile price change = 2.33*3.16%*100 = $7.37
SPAN Model
Span Risk (based on historical data)
16 Scenarios
Intra-Commodity Charge
Inter-Commodity Credit
Short-Option Minimum
T – Copula models
Financial instruments exhibit a higher frequency of extreme values (fat tails)
than a normal distribution.
Normal Distribution Curve
T Distribution Curve
For an individual instrument, historical data can be used to fit the data into
a T distribution
For a portfolio of instruments, a T copula is used to capture the tail
correlation between the different instruments
Simple Historical Simulation
Changes in risk factor for each day is considered a shock
Example:
Current Price = $100
Day
Price
Shock
Forecasted Price
PnL
1
78
-0.02532
97.4682192
-2.53178
2
85
0.085942
108.594243
8.594243
3
90
0.057158
105.715841
5.715841
Filtered Historical Simulation
• We would like to give more weight to recent shocks.
• Scale returns by ratio of current volatility/volatility at the time of shock
Example (from attached Excel)
EWMA volatility scaling
One of the big advantages of historical simulation is that we need not
make any
Assumption regarding the parametric distribution of risk factors.
Correlation between risk factors is implicit.
Easy to implement
Shocks are confined to past history
IM generated from filtered HS may exhibit pro-cyclicality
Extreme Value Theory (EVT)
Only the extreme shocks are modeled. May result in much higher IM.
Example from attached Excel
Standard Initial Margin Model (SIMM): ISDA Proposal
Standard ISDA model for CDS is widely used
ISDA has identified the following criteria for building a standard model that
Can be used by all market participants for un-cleared swaps
Non-procyclical
Ease of replication
Transparency
Quick to calculate
Extensible Methodology
Predictability
Costs
Margin appropriateness
SIMM Model
Compute IM based on the first order sensitivities of a portfolio to a standardize
set of risk factors.
Risk factors are classified into four broad asset classes:
• Currencies/rates
• Equities
• Credit
• Commodities
Example
Interest Rate Portfolio of 1000 positions
Compute delta ladder (DV01 values at different points).
TENOR (YRS)
DV01
TENOR (YRS)
SHOCK
0.25
0.5
1
2
5
7
10
15
20
25
30
($49,971) $298,655 $949,842 $1,388,557 ($1,288,234) ($3,318,529) ($2,672,599) $1,942,351 $22,127 ($471,705) ($2,245,130)
0.25
-4
0.5
0
1
-1
2
-3
5
-6
7
-12
10
-16
15
-17
20
-17
25
-16
30
-17
TENOR (YRS)
0.25
0.5
1
2
5
7
10
15
20
25
30 TOTAL
PnL
$190,250 ($144,214) ($1,398,927) ($4,327,716) $8,063,958 $38,488,631 $41,905,285 ($32,242,834) ($365,105) $7,771,475 $37,773,866 $95,714,668
Issues with SIMM model
• Assumes that sensitivities are given. Does not cover how sensitivities
are calculated.
• Different models will produce different deltas
• Risk sensitivities are very difficult to compute
• Base currency of computation
Variation Margin
Daily P&L of a position. Measured by change in daily MTM
Futures and Options on Futures
• Futures P&L = Change in price *contract size*# of contracts
ex: For a 10 long positions in a wheat contract, a daily price
change of $-0.50; P&L = -$0.5*10*5000 = -$25000
• Option P&L = Option delta*change in underlying*contract size*
# of contracts
ex: If you have sold 10 option contracts for the above, and option
delta =0.6: P&L =-0.6* -$0.5*10*5000 = -$25000 =$15,000
Interest Rate Swap
P&L = Daily change in NPV of swap
Accumulated Interest
PAI
Credit Default Swaps (CDS)
• Current value of swap may be given as a market spread
• Need to convert spreads prices
• ISDA model
Minimum Considerations
• Counterparty setup & Client onboarding
• Trade Execution
• IM and VM calculation
• Collateral eligibility
• Segregation