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# Complex Match Example

The diagram shows the order book sources used in this example. GE products (Eurodollars) are on the A (Pro Rata) algorithm and have a Pro Rata minimum of 2.

The steps are: ### Scenario

In this example, the total GEZ9 bid size is 2000, 1000 of which is real resting quantity. The other 1000 lots are implied from four other sources.

Sources are:

1. GEZ9 resting, 1000 lots
2. GEZ9-GEH0 and GEH0, 200 lots
3. GEZ9-GEM0 and GEM0, 300 lots
4. GEZ9-GEU0 and GEU0, 400 lots
5. GEZ9-GEZ0 and GEZ0, 100 lots

TOP orders are present in GEZ9, GEM0, and GEZ9-GEZ0.

Sequence

Given the above, when an aggressing order for 501 arrives in GEZ9, the following steps occur:

Steps 1-6 below predetermine allocation quantities. Following predetermination, matches for each instrument are processed using the appropriate algorithm once per instrument. Step 3 below rounds down since the instruments traded do not include ICS ratio spreads.
1. Check the aggressed resting source for a TOP.  If TRUE (as in this example), add quantity to the aggressed source and subtract the same quantity from the aggressing quantity.
• Source #1 receives 100 lots.
• Sources #2 through #5 receive no lots in this step.
• The aggressing quantity is reduced from 501 to 401 from the 100 lot distribution for TOP.
2. Aggressing quantity remains, so proceed to next step of the algorithm with 401 aggressing.
3. The next step is Pro-Rata. Distribute quantity to sources using this formula: (resting remaining source quantity)/(total available quantity from all sources)*aggressing quantity ≥ 2 = allocation to source
• Source #1 = 900/1900*401>=2 = 189
• Source #2 = 200/1900*401>=2 = 42
• Source #3 = 300/1900*401>=2 = 63
• Source #4 = 400/1900*401>=2 = 84
• Source #5 = 100/1900*401>=2 = 21

4. Total allocated during Pro-Rata is 189+42+63+84+21 = 399. There are two lots left over due to rounding. These are distributed to the aggressed instrument. In the event that the resting book is filled or missing at this point, these lots would go to the earliest expiry source. From the above example, this would be the source containing the spread GEZ9-GEH0 since H0 is the earliest expiry available.

5. Final source distribution from predetermination:

• Source #1 = 100+189+2 = 291
• Source #2 = 42
• Source #3 = 63
• Source #4 = 84
• Source #5 = 21

6. Since each source (except for the resting source) is composed of two instruments, CME Globex assigns like quantities to each component of the source. Final breakdown of aggressing quantities for each instrument is:

• GEZ9 = 291
• GEZ9-GEH0 = 42
• GEH0 = 42
• GEZ9-GEM0 = 63
• GEM0 = 63
• GEZ9-GEU0 = 84
• GEU0 = 84
• GEZ9-GEZ0 = 21
• GEZ0 = 21

7. With all instrument quantity allocation accounted for, CME Globex resolves a match for each instrument using the appropriate algorithm for each instrument with the quantities determined in step 6.

### Source Allocations

#### Source #1: GEZ9 = 291 aggress

TOP order gets 100 and is filled. 191 left to match.

Pro Rata now matches with this formula (display order qty)/(total qty) * (match qty) >=2 = allocation

Order 2 = 200/900*191 = 42

Order 3 = 300/900*191 = 63

Order 4 = 400/900*191 = 84

42+63+84 = 189, 2 lots left for next step which is FIFO. This goes to Order 2.

Final Resting Book GEZ9

Order

Working Quantity

2

156

3

237

4

316

#### Source #2: GEZ9-GEH0 spread = 42 aggress

No TOP.

Pro Rata

Order 1 = 50/200*42 = 10

Order 2 = 25/200*42 = 5

Order 3 = 75/200*42 = 15

Order 4 = 50/200*42 = 10

10+5+15+10 = 40, 2 lots left over for FIFO which goes to Order 1.

Final Resting Book GEZ9-GEH0

Order

Working Quantity

1

38

2

20

3

60

4

40

#### Source #2: GEH0 = 42 aggress

No TOP.

Pro Rata

Order 1 = 20/200*42 = 4

Order 2 = 60/200*42 = 12

Order 3 = 80/200*42 = 16

Order 4 = 40/200*42 = 8

4+12+16+8 = 40, 2 lots left over for FIFO which goes to Order 1.

Final Resting Book GEH0

Order

Working Quantity

1

14

2

48

3

64

4

32

#### Source #3: GEZ9-GEM0 = 63 aggress

GEZ9-GEM0

Bid

1

90

2

80

3

70

4

60

No TOP.

Pro Rata:

Order 1 = 90/300*63 = 18

Order 2 = 80/300*63 = 16

Order 3 = 70/300*63 = 14

Order 4 = 60/300*63 = 12

18+16+14+12=60, 3 lots left over which goes to order 1.

Final resting book after all allocations:

GEZ9-GEM0

Bid

1

69

2

64

3

56

4

48

#### Source #3: GEM0 = 63 aggress

GEM0

Bid

1

50T

2

75

3

75

4

100

TOP order gets the first 50 lots, leaving 13 for the next step.

Pro Rata:

Order 2 = 75/250*13 = 3

Order 3 = 75/250*13 = 3

Order 4 = 100/250*13 = 5

3+3+5=11, 2 lots left over which goes to order 2.

Final resting book after all allocations

GEM0

Bid

2

70

3

72

4

95

#### Source #4: GEZ9-GEU0 = 84 aggress

GEZ9-GEU0

Bid

1

75

2

150

3

50

4

125

No TOP.

Pro Rata:

Order 1 = 75/400*84 = 15

Order 2 = 150/400*84 = 31

Order 3 = 50/400*84 = 10

Order 4 = 125/400*84 = 26

15+31+10+26=82, 1 lot left over which goes to order 1.

Final resting book after all allocations:

GEZ9-GEU0

Bid

1

59

2

119

3

40

4

99

GEU0 = 84

GEU0

Bid

1

130

2

125

3

70

4

75

No TOP.

Pro Rata:

Order 1 = 130/400*84 = 27

Order 2 = 125/400*84 = 26

Order 3 = 70/400*84 = 14

Order 4 = 75/400*84 = 15

27+26+14+15=82, 1 lot left over which goes to order 1.

Final resting book after all allocations:

GEU0

Bid

1

102

2

99

3

56

4

60

#### Source #5: GEZ9-GEZ0 = 21 aggress

GEZ9-GEZ0

Bid

1

10T

2

40

3

20

4

30

TOP order gets the first 10 lots, with 11 remaining going to the next step.

Pro Rata:

Order 2 = 40/100*11 = 4

Order 3 = 20/100*11 = 2

Order 4 = 30/100*11 = 3

4+2+3=9, 2 lots left over which goes to order 2.

Final resting book after all allocations:

GEZ9-GEZ0

Bid

2

34

3

18

4

27

#### Source #5: GEZ0 = 21

GEZ0

Bid

1

20

2

10

3

5

4

65

No TOP.

Pro Rata:

Order 1 = 20/100*21 = 4

Order 2 = 10/100*21 = 2

Order 3 = 5/100*21 = 1 which becomes 0 due to the Pro Rata Min for this product.

Order 4 = 65/100*21 = 13

4+2+1+13=20, 1 lot left over which goes to order 1.

Final resting book after all allocations:

GEZ0

Bid

1

15

2

8

3

5

4

52