Hybrid Pro-Rata/Time Matching

Install and import#

npm install fintech-algorithms

import { hybridProRataTime } from "fintech-algorithms/matching-engines-and-venue-logic/continuous-matching/hybrid-pro-rata-time-matching";

Signature#

hybridProRataTime(incomingRaw, priceRaw, lotRaw, fractionRaw, restingRaw)

Splits an incoming order between a time-priority portion and a pro-rata portion — the compromise most futures venues actually run, because pure pro-rata invites size inflation and pure price-time invites a latency race.

Parameters#

Returns#

{ model, price, lot_size, fifo_fraction, incoming_quantity, executable_quantity, fifo_target_quantity, pro_rata_target_quantity, allocated_quantity, unfilled_quantity, allocations, state }

Both target quantities, and allocations ordered by arrival with each order's fill split into fifo_quantity and pro_rata_quantity. state is fully-allocated or partially-allocated.

Errors#

• When fractionRaw is below zero or above one — throws RangeError

Complexity: time O(resting log resting), space O(resting).

Worked example#

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input#

600

100

1

0.4

[
  {
    "order_id": "H-1",
    "side": "sell",
    "price": 100,
    "remaining_quantity": 500,
    "arrival_sequence": 10
  },
  {
    "order_id": "H-2",
    "side": "sell",
    "price": 100,
    "remaining_quantity": 300,
    "arrival_sequence": 20
  },
  {
    "order_id": "H-3",
    "side": "sell",
    "price": 100,
    "remaining_quantity": 200,
    "arrival_sequence": 30
  }
]

Call#

hybridProRataTime(incomingRaw, priceRaw, lotRaw, fractionRaw, restingRaw)

Returns#

object with 12 fields: model, price, lot_size, fifo_fraction, incoming_quantity, executable_quantity, fifo_target_quantity, pro_rata_target_quantity, …

{
  "model": "single-price-fifo-pro-rata-split",
  "price": 100,
  "lot_size": 1,
  "fifo_fraction": 0.4,
  "incoming_quantity": 600,
  "executable_quantity": 600,
  "fifo_target_quantity": 240,
  "pro_rata_target_quantity": 360,
  "allocated_quantity": 600,
  "unfilled_quantity": 0,
  "allocations": [
    {
      "order_id": "H-1",
      "resting_quantity": 500,
      "fifo_quantity": 240,
      "pro_rata_quantity": 123,
      "allocated_quantity": 363,
      "remaining_quantity": 137,
      "arrival_sequence": 10
    },
    {
      "order_id": "H-2",
      "resting_quantity": 300,
      "fifo_quantity": 0,
      "pro_rata_quantity": 142,
      "allocated_quantity": 142,
      "remaining_quantity": 158,
      "arrival_sequence": 20
    },
    {
      "order_id": "H-3",
      "resting_quantity": 200,
      "fifo_quantity": 0,
      "pro_rata_quantity": 95,
      "allocated_quantity": 95,
      "remaining_quantity": 105,
      "arrival_sequence": 30
    }
  ],
  "state": "fully-allocated"
}

Other exports#

This module also exports priceTimePriority, proRataMatching, sizeTimePriority, calculate. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams#

Calculation flow#

flowchart LR
    S1["Validate the oneprice book and fraction"]
    S2["Compute executable whole lots"]
    S3["Floor the FIFO target and allocate oldest orders first"]
    S4["Recompute residual resting capacity"]
    S5["Allocate the remaining target pro rata and reconcile"]
    S1 --> S2
    S2 --> S3
    S3 --> S4
    S4 --> S5
    S5 --> D{"zeroone split endpoints and capacity doublecount preventio"}
    D --> O["allocated_quantity + diagnostics"]
    O --> A["Audit: FIFO and prorata targets sum to executable quantity"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• How CME Group Agricultural Markets Operate — CME Group
• Matching Algorithm Overview — CME Group
• Matching principles — Eurex Frankfurt AG
• Evidence boundary

The rest of the Continuous Matching family#

• Price-Time PriorityMatches an incoming order against resting orders by best price, then earliest arrival.
• Pro-Rata MatchingAllocates a fill across all resting orders at a price in proportion to size, ignoring arrival time.
• Size-Time PriorityOrders by size first and arrival second — rewarding large resting orders.