# CME Order Matching Algorithms. Part 4

Dear friends! Today, we will consider the operation of the threshold algorithm of proportional distribution with the use of the market maker stimulation program (Threshold Pro Rata with LMM) through the example of the US 10-Year Treasury Note option.

• Logic of the algorithm operation.
• Example of use.

Threshold Pro Rata with LMM algorithm is a modified Pro Rata algorithm. This algorithm firstly provides the priority to that limit order, which was posted the first one at the best price level. The aggressive orders, which enter the market, are allocated with this top order as a matter of priority and in the maximum amount, envisaged for a specific instrument. After that, allocation in accordance with the LMM principle takes place. The next stage is the Pro Rata allocation. The residue of the aggressive order amount is processed by the FIFO algorithm.

That is, in fact, the Threshold Pro-Rata with LMM algorithm passes the following stages of allocation:

• Allocation of the TOP order with the set allocation minimum and/or maximum.
• LMM (the Lead Market Maker program).
• Pro Rata (proportional distribution).
• FIFO (First In, First Out) for any residual amount.

The Threshold Pro Rata with LMM algorithm is used in the markets of such trading instruments as 10-Year middle-term Treasury Note options, Bloomberg Commodity index futures and long-term Treasury Note options.

## Algorithm application through the example of the 10-year us treasury note option

Let’s consider the algorithm operation through the example of the US 10-Year Treasury Note option with the OZNH7C ticker. Let’s assume that the latest price, at which the instrument was traded, is 24’22.

After which, three sell orders got into the system for selling at the price of 24’21: Sell Limit for 300 contracts, Sell Limit for 15 contracts and Sell Limit for 160 contracts. The order that was the first to get into the system will be identified by the algorithm as the TOP order and, consequently, it will receive the highest priority during execution.

The key parameters of order matching for the 10-Year Treasury Note option are the following:

• The top order is allocated in the amount of 100% provided its size is not less than 25 contracts (if the top order size is below the threshold value, the algorithm will not allocate it) and not more than 250 contracts (if the top order size exceeds 250 contracts, the order is allocated partially in the amount of the maximum value, which is set in the algorithm).
• Pro Rata envisages the minimum allocation equal to 1.

Let’s consider in detail what would happen at the new Best Ask 24’21 level of the general size of 300+15+160=475 contracts.

The order with the HOM identifier is located as the first one in the order book at the level of the best price of 24’21 and this is why it gets the highest priority.

The HOM limit order will be allocated in the amount of 250 contracts since 250 is the maximum, envisaged by the algorithm for the trading instrument under our consideration.

The ZNC order was identified by the system as an LMM order with 40% allocation. 40% from the remaining 150 contracts of the aggressive order equals 60. Consequently, these 60 contracts will get priority in accordance with the LMM conditions.

As we already know from the previous articles about the CME Group order matching algorithms, the size of every limit order in the Pro Rata cycle is divided into the general size of all the orders, which are located at the best price level under our consideration, for finding Pro Rata ratios.

After which, the received ratios are multiplied by the general size of all the orders. The results are rounded. The residue of the aggressive order volume in the amount of 90 contracts are distributed among limit orders by the Pro Rata algorithm. As a result, the HOM order is allocated in the amount of 27 contracts, PRO – 8 contracts and ZNC – 54 contracts.