# SA Securities

Initially, SPAN® was developed for derivatives margining and has become a well-known standard in this domain. Since 12th of January 2001, SPAN® method is used for securities margining (equities and bonds) as well.

SPAN® Cash Brochure

Positions used for calculation

Calculation of a net position for each security. For each account, a single net buying or selling position is calculated for all the settlement dates of each security.

Example : Calculation of the net position for a given security and clearing member‘s accounts.

SA Securities
'house' Position Account' 10 25
'falls' Position Account 30 25

We therefore have respectively a net selling position of 15 and a net buying positions of 5.

Valuation of net positions per security. The buying/selling position calculated is valuated with :

• the reference settlement price for equities

• the settlement price times the modified duration for bonds

For a given account and a given security i position, there is a valuated buying position (BPi) or selling position (SPi).

Example :

No of Bonds Side (B/S) Price BPi SPi

Stock 1

10

S

150

€1500

Stock 2

10

B

200

€4000

Stock 3

5

S

170

€650

Stock 4

30

B

50

1500

No of Bonds Side (B/S) Price Modified Duration BPi SPi

Bond 1

2

B

500

2.5

€2500

Bond 2

10

B

200

3

€6000

• Determination of the basis for the risk calculation : each security is linked to a so-called "Business Function Combined Commodities" (1) ("BFCC") ; the basis for the liquidation risk calculation is the sum of the valuated net buying positions and selling positions per BFCC.

In the previous example, if the stocks 1,2,3,4 are all linked to the same BFCC, we get :

= 5 500 euros and = 2 350 euros

If the bonds belong to the same BFCC, we have :

= 8 500 euros and = 0

Liquidation risk calculation:

The algorithm for calculating the liquidation risk for each BFCC (and for a given account) is the following :

Liquidation risk =

The coefficients x% (specific or credit risk) and y% (general market or interest rates shift risk) are determined per BFCC.

Additional coefficients are available to take into account :

• risks offsetting between different BFCC made up of similar securities (risk decrease coefficients called INTER) ;

• the need to cover yield curve twist risk (residual risk) between bonds belonging to the same BFCC (risk increase coefficients called : INTRA). This coefficient is only used for bonds.

All coefficients are parameters that can be reviewed depending on market conditions.

Example: calculation for bonds (modified duration method)

Step 1: Calculation of Liquidation Risk for each BFCC using the coefficients y% (general variation of the interest rate) and x% (specific risk).

Example:

(x%;
y%)

LR
BFCC1 (0%;1%) 50,000 120,000 700 0 700
BFCC2 (0%;1%) 130,000 100,000 600 2,300 2,900
BFCC3 (1%;3%) 190,000 90,000 3,000 2,800 5,800

Step 2 : Calculation of the Residual Risk. The risk is calculated by applying an increase coefficient INTRA to the positions in a single BFCC that have been offset in step 1.

Residual Risk =

INTRA coef. x Min (, )

Example:

Coefficient

Min(,) RR LR + RR
BFCC1 0.5% 50,000 +250 950
BFCC2 1% 100,000 +1,000 3,900
BFCC3 (1%;3%) 90,000 +450 6,250

Step 3 : Risk decrease calculation between different BFCC (INTER coefficient).

Decrease (BFCC1/BFCC2) =

INTER coef. x Min (,)

Side (B/S)

Priority 1

Priority 2 Priority 3 Decrease LR + RR - Decrease
BFCC1 S 70,000 1% * 30,000   0.5% * 40,000 -500 450
BFCC2 B 30,000 1% * 30,000     -300 3,600
BFCC3 B 100,00     0.5% * 40,000 -200 6,050

Order of priority :
Priority 1 : BFCC1 / BFCC2 INTER coefficient 1%
Priority 2 : BFCC2 / BFCC3 INTER coefficient 1%
Priority 3 : BFCC1 / BFCC3 INTER coefficient 0,5%

Step 4 : The total initial margin is the sum of the risks for each BFCC.
In the above example, the initial margin is : 450 + 3 600 + 6 050 = 10 100 euros
Parameters used in examples just intend to explain the calculation mecanism and do not reflect the actual coefficient to be adopted after a fair amount of analysis and statistical work. It is intended to define 9 classes ("BFCC") crossing 3 modified duration ranges and 3 sets of issuer rating.

Standard Plan Level 1 (\$) 250bn - 750bn Level 2 (\$) 750bn - 1.5m Level 3 (\$) 1.5m +
Transaction maturity 0% -15% -25% -35%
0 - 1 year 0.9 0.77 0.68 0.59
1 year - 3 years 2.25 1.91 1.69 1.46
3 years - 5 years 4.05 3.44 3.04 2.63
5 years - 7 years 5.4 4.59 4.05 3.51
7 years - 10 years 7.2 6.12 5.40 4.68
10 years - 12 years 8.89 6.89 6.08 5.27
12 years - 15 years 9 7.65 6.75 5.85