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%

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%

Standardized haircut schedule

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 standardized

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).

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

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

TENOR (YRS) 0.25 0.5 1 2 5 7 10 15 20 25 30

SHOCK -4 0 -1 -3 -6 -12 -16 -17 -17 -16 -17

TENOR (YRS) 0.25 0.5 1 2 5 7 10 15 20 25 30

DV01 ($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)

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