Price-Time Priority Order Matching Engine for Auctions

This is an attempt to implement a simplified version of the order matching engines used in auctions (e.g. during opening or closing) on major exchanges.

Current limitations:

• Only Limit Orders are supported

Auction Phases

Phase 1: Book Building

In this first phase an order book is open and accepts new orders. Orders may also be modified/amended or cancelled.

Phase 2: Price Determination Phase

Once Matching is initiated, order book is closed and no more orders are accepted.

First of all, orders are grouped and sorted by

1. Side: Buy (Bid) or Sell (Ask)
2. Limit Price: Buy orders with higher limit price and Sell orders with lower limit price have higher priority for execution (price priority). In case of multiple orders having the same limit price, orders which arrived earlier (time priority) have higher priority.

Next, total volume for each price point is determined on both sides of the order book (Bid and Ask).

Total volumes are summed up from the top of the order book to build aggregate supply and demand for each price level.

Finally, from the minimum values of supply and demand aggregates, the maximum executable volume is determined across all price levels.

Phase 3: Execution Phase

Provided the execution price and the execution volume determined in the previous phase, the orders can be executed. The rules specified above ensure that maximum of one order can be partially executed on either side of the order book. All other orders would either be fully executed or would remain open with full size.

Example

Consider the following order book before the start of Phase 2:

Order	Bid Quantity	Bid Price	Ask Price	Ask Quantity	Order
B1	100	104.5	100.5	600	S1
B2	2500	104.5	100.5	400	S2
B3	1800	103	102	1500	S3
B4	500	102.5	103	1200	S4
B5	800	102.5	104.5	700	S5
B6	1500	99.5	--	--	--

Combining price levels from bid and ask, grouping orders and calculating total and aggregate supply & demand yields the following result:

Buy Orders	Aggregate Demand	Total Demand	Price	Total Supply	Aggregate Supply	Sell Orders
B1, B2	2600	2600	104.5	700	4400	S5
B3	4400	1800	103	1200	3700	S4
B4, B5	5700	1300	102.5	0	2500	--
--	5700	0	102	1500	2500	S3
--	5700	0	100.5	1000	1000	S1, S2
B6	7200	1500	99.5	0	0	--

Aggregation is done from top to bottom on the bid side and from bottom to top on the ask side (i.e. always from the best price on either side). To find the maximum executable volume, one needs to look at the aggregate supply and demand values across all price levels and find the max. For this purpose we need to consider the min of both aggregate values (supply and demand) since only so much can be satisfied for any given price level. In this case our auction price is determined as 103 and our max execution volume is 3700 (=min of 3700 and 4400).

Once these two values have been determined, we can go back to Table 1 and proceed with order execution:

Execution Price: 103

Order	Execution	Bid Quantity	Bid Price	Ask Price	Ask Quantity	Execution	Order
B1	100	100	104.5	100.5	600	600	S1
B2	2500	2500	104.5	100.5	400	400	S2
B3	1100	1800	103	102	1500	1500	S3
B4	0	500	102.5	103	1200	1200	S4
B5	0	800	102.5	104.5	700	0	S5
B6	0	1500	99.5	--	--	--	--