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Margin Calculationss
Introduction
This document shows an example of the calculations used to determine the margin requirement of a simple
Forex portfolio containing Forex Spot and Forex Option positions. It contains examples of how to calculate
Delta Margin, Vega Margin and how they shall be combined to find the total margin requirement for the
portfolio.
Positions
The Forex Spot and Forex Option positions shown in Table 1 represent the Sample Forex portfolio for which
the Portfolio Margin Requirement will be calculated.
Table 1 – Example of Forex Spot and Forex Option positions of a Forex portfolio.
L/S
Type
S
Spot
S
Option
S
L
put/call
Amount
Ccy pair
Strike
1,000,000
EURCHF
Call
500,000
EURUSD
1.4055
Option
Call
1,000,000
USDCHF
Option
Call
1,000,000
GBPUSD
L
Option
Call
1,000,000
S
Option
Put
500,000
Expiry Date
Delta
Implied
Volatility
Vega
Volatility
Factor
1
0
1 Month
0.5123
USD -815
0.2624
11%
1.0980
1 Month
0.5082
CHF -1,274
0.2493
11%
1.0520
1 Month
0.5097
USD 1,742
0.2401
11%
USDCHF
1.0990
1 Week
0.5116
CHF 607
0.2549
28%
GBPUSD
1.4980
1 Month
-0.4955
USD -868
0.2400
11%
Delta Margin
The tables, descriptions and calculation examples below illustrate how the Delta Margin requirement for
the above mentioned Forex portfolio is calculated.
1. The Delta Exposure in the first currency (i.e. Ccy1; EUR in EURUSD) is calculated for every Forex
Spot and Forex Option position in the Forex portfolio. The Delta of a Forex Spot position is 1 (or
100%).
If a position is sold, the amount needs to be multiplied by -1. If a position is bought it needs to be
multiplied with 1. Therefore we get 2 formulas:
For short positions: DELTA EXPOSURE = NOTIONAL AMOUNT *DELTA * (-1)
For long positions: DELTA EXPOSURE = NOTIONAL AMOUNT * DELTA * 1
Example calculation for the EURUSD Forex Option call position (using the data from Table 1.
Specific data about a portfolio can be found under “position details” in the account summary):
 500,000 * 0.5123 *(-1) = EUR -256,150
This Ccy 1 Delta Exposure can also be found for each position in the account summary.
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Table 2 – Delta exposures for the Forex Spot and Forex Option positions.
Cross
Delta Exposure Ccy1
Delta exposure Ccy2
Current spot rates
EURCHF
-1,000,000
1,541,910
EURCHF 1.54191
EURUSD
-256,150
358,830
EURUSD 1.40086
USDCHF
-508,200
559,416
USDCHF 1.10078
GBPUSD
509,700
-762,837
GBPUSD 1.49664
USDCHF
511,600
-563,159
USDCHF 1.10078
GBPUSD
247,750
-370,793
GBPUSD 1.49664
2. The values for the value for the Delta Exposure (Ccy1) are shown in Table 2. The Ccy2 (USD in
EURUSD) exposure is depending on the current spot rate. When switching from base to quoted
currency, the sign changes (when a trader is short notional EURUSD he/she is short EUR and long
USD). This is done with a multiplication of -1.
CCY 2 EXPOSURE = Ccy1*(-1)* CURRENT SPOT RATE
3. The net single currency delta exposures are calculated across all the positions, by adding all
exposures together per currency.
Example calculation for the USD delta exposure (using the data from Table 2):
 358,830 + (-508,200) + (-762,837) + 511,600 + (-370,793) = USD -771,400
This is the value for the Net Delta Exposure for USD shown in Table 3.
4. These net single currency delta exposures are converted into the account currency (USD for this
Forex portfolio example) using the current spot rate.
Translating a Ccy1 exposure to the account currency, using the example calculation for the EUR
exposure (with data from Table 3):
USD EXPOSURE = NET DELTA EXPOSURE Ccy1 * CURRENT EURUSD SPOT RATE
 -1,256,150 * 1.40086 = USD -1,759,690
This is a short position, and therefore USD 1,759,690 is added to the Short Position USD equivalent
in Table 3.
Translating a Ccy2 exposure to account value, using the example calculation for the CHF exposure
(with data from Table 3):
USD EXPOSURE = NET DELTA EXPOSURE Ccy2 / CURRENT USDCHF SPOT RATE
 1,538,167 / 1.10078 = USD 1,397,343
This is a long position, and therefore USD 1,397,343 is added to the Long Position USD equivalent in
Table 3.
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Table 3 – Net single currency delta exposures for the Forex portfolio and separated
USD equivalent long and short positions and their absolute totals.
Net Delta
Long positions
Short Positions
Currency Exposure
Current spot rates
(USD equivalent)
(USD equivalent)
EUR
-1,256,150
EURUSD 1.40086
0
1,759,690
CHF
1,538,167
USDCHF 1.10078
1,397,343
0
GBP
757,450
GBPUSD 1.49664
1,133,630
0
USD
-771,400
0
771,400
5. To find the Delta Margin requirement of the Forex portfolio each exposure needs to be multiplied
with the required margin for that currency. As this sample portfolio only contains major currencies,
all USD equivalent amounts are multiplied with 1% (when this example was created the margin
requirement, which can, be found in the FX rates and conditions, was 1% for majors). This is
summarized in Table 4.
For each exposure the following calculation is therefore applied:
MARGIN REQUIREMENT = DELTA EXPOSURE * FOREX SPOT MARGIN REQUIREMENT
Table 4 – Margin Requirement summarized for long and short exposure.
Delta exposure long Delta exposure
positions (USD
short positions
Margin requirement for Margin requirement for
Currency equivalent)
(USD equivalent)
long positions (USD)
short positions (USD)
EUR
0
1,759,690
0
17,597
CHF
1,397,942
0
13,979
0
GBP
1,133,630
0
11,336
0
USD
0
771,400
0
7,714
25,315
25,311
6. The Margin Requirement for longs and short respectively are summed and the largest of the two
represents the Delta Margin Requirement for the portfolio.
USD 25,315 > USD 25,311  The Delta Margin requirement is USD 25,315.
Vega Margin
The vega margin calculation is designed to reflect the potential loss in the value of positions due to changes
in volatility. This can be summarized as follows: for long positions there is a loss from a decrease in volatility,
while for short positions there is a loss from an increase in volatility.
The example below is based on the example portfolio listed on page 1.
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1. The Vega Exposure for each Forex Option position is calculated based on the change in value for a 1%
(100 basis points) increase in implied volatility. The Vega of a Forex Spot position is 0 so these do
not have a Vega Margin requirement.
VEGA EXPOSURE = NOTIONAL AMOUNT * VEGA
The Vega Exposure can be found for each position in the account summary.
2. To find the Vega Margin though, one has to multiply the Vega Exposure with the Implied Volatility
and the Volatility Factor. The Implied Volatility can be found for each position in the account
summary. The volatility factor however needs to be interpolated by using table 5 below, depending
on time to expiry and the currency pair.
Table 5 – Volatility Factor table.
Tenor
1 week
2 weeks
1 month
3 months
1 year
Days
7
14
30
90
365
Major currency pairs
Minor currency pairs
28%
50%
20%
25%
11%
20%
8%
15%
8%
10%
VEGA MARGIN = (VEGA EXPOSURE * 100) * IMPLIED VOLATILITY * VOLATILITY FACTOR
In the mentioned example portfolio the Vega margin for the short EURUSD Call option is:
 (-815 * 100) * 0.2624 * 0,11 = -2,352 USD
The Vega margin needs to be calculated for each position.
Table 6 – Vega Margin for the Forex Option positions in the sample portfolio.
Ccy pair
EURUSD
Expiry date
1 Month
Vega Margin
USD-2,352
Current spot rate
Vega Margin
(USD equivalent)
-2,352
-2,352
USDCHF
1 Month
CHF -3,494
USDCHF 1.10078
-3,174
-3,174
GBPUSD
GBPUSD
1 Month
1 Month
USD 4,601
USD -2,292
4,601
-2,292
2,309
USDCHF
1 Week
CHF 4,332
USDCHF 1.10078
3,936
3,936
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3. The Vega Margin requirement for each position is converted into the account currency (USD for
this Forex portfolio) using the current spot rate
Example calculation for the 1M USDCHF position (using the data from Table 6):
 -3,494 / 1,10078 = USD -3,174
4. The Vega Margin requirements in the account currency are netted for each currency pair and exact
expiry date.
Example Calculation for the GBPUSD 1 Month positions (using the data from Table 6):
 4,601 + (-2,292) = USD 2,309
This is the value of the Vega Margin (USD Equivalent) for the GBPUSD 1 Month Forex Option
positions shown in Table 6.
5. The Vega Margin requirement for the Forex portfolio is the sum of the absolute value of the netted
(by currency pair and expiry date) Vega Margin requirements.
Value of the Vega Margin in USD (using the data from Table 6):
 2,352 + 3,174 + 2,309 + 3,936 = USD 11,771
Portfolio Margin Requirement
This section shows how the Delta Margin and Vega Margin requirements are combined to determine the
Portfolio Margin Requirement for the sample Forex portfolio.
1. The Delta Margin and Vega Margin requirements in the account currency are summed to
determine the total margin required.
MARGIN REQUIRED = DELTA MARGIN + VEGA MARGIN (using the data derived in previous sections):
 25,315 USD + 11,771 USD = 37,088 USD
2. Across Forex products, the margin rates for the first EUR 50,000 of investment collateral are 50% of
the normal margin rates. This “double equity” level must be taken into consideration to determine
the Portfolio Margin Requirement for the Forex portfolio.
In this example EURUSD is trading at 1.40086 which gives a double equity amount of USD 70,043.
As USD 37,088 < USD 70,043 the margin reserved on this sample account is USD 37,088 / 2 = USD
18,544.
3. To calculate the Margin Utilization used on the account. For below example an account value of
USD 50,000 has been used and the assumption made that no other positions apart from above
mentioned Forex Portfolio is held on the account.
MARGIN UTILIZATION = USED FOR MARGIN REQUIREMENT / NET EQUITY FOR MARGIN (These
numbers can be found in the Account Summary)
USD 18,544 / USD 50,000 = 0.37088 ≈ 37%
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