Percentage-of-Volume Execution

Install and import#

npm install fintech-algorithms

import { percentageOfVolumeExecution } from "fintech-algorithms/execution-and-transaction-cost-analysis/schedule-based-execution/percentage-of-volume-execution";

Signature#

percentageOfVolumeExecution(total_quantity, participation_rate_bps, market_volume_buckets, lot_size, max_child_quantity)

Trades a fixed share of whatever volume occurs. The schedule is unknown in advance by design, which limits impact — and means the order may not complete at all if volume never arrives.

Parameters#

Returns#

{ schedule, projected_completion, unfilled_quantity, … }

The schedule with projected completion and any quantity the volume path cannot absorb.

Errors#

• When the participation rate is not positive — throws

Complexity: time O(buckets), space O(buckets).

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#

10000

1000

[5200, 4600, 4100, 3800, 3500, 3300]

Showing 6 of 24 elements.

100

700

Call#

percentageOfVolumeExecution(total_quantity, participation_rate_bps, market_volume_buckets, lot_size, max_child_quantity)

Returns#

object with 10 fields: total_quantity, participation_rate_bps, lot_size, max_child_quantity, observed_market_volume, released_quantity, remaining_quantity, achieved_participation_bps, …

{
  "total_quantity": 10000,
  "participation_rate_bps": 1000,
  "lot_size": 100,
  "max_child_quantity": 700,
  "observed_market_volume": 120900,
  "released_quantity": 10000,
  "remaining_quantity": 0,
  "achieved_participation_bps": 827.129859,
  "schedule": [
    {
      "bucket": 1,
      "market_volume": 5200,
      "cumulative_market_volume": 5200,
      "target_cumulative_quantity": 500,
      "child_quantity": 500,
      "released_cumulative_quantity": 500,
      "remaining_quantity": 9500,
      "achieved_participation_bps": 961.538462
    },
    {
      "bucket": 2,
      "market_volume": 4600,
      "cumulative_market_volume": 9800,
      "target_cumulative_quantity": 900,
      "child_quantity": 400,
      "released_cumulative_quantity": 900,
      "remaining_quantity": 9100,
      "achieved_participation_bps": 918.367347
    },
    {
      "bucket": 3,
      "market_volume": 4100,
      "cumulative_market_volume": 13900,
      "target_cumulative_quantity": 1300,
      "child_quantity": 400,
      "released_cumulative_quantity": 1300,
      "remaining_quantity": 8700,
      "achieved_participation_bps": 935.251799
    }
  ],
  "state": "parent-complete"
}

Other exports#

This module also exports twapExecution, historicalVwapExecution, adaptiveVwapExecution, 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 parent rate volume basis lot and child cap"]
    S2["Accumulate observed market volume"]
    S3["Compute lotfloored cumulative target"]
    S4["Release the smaller of deficit cap and parent residual"]
    S5["Report achieved participation and completion"]
    S1 --> S2
    S2 --> S3
    S3 --> S4
    S4 --> S5
    S5 --> D{"target deficit equal to zero child cap and parent completi"}
    D --> O["released_quantity + diagnostics"]
    O --> A["Audit: Released quantity never exceeds the parent"]

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#

• Execution and Block Trade Pricing with Optimal Constant Rate of Participation — Olivier Guéant
• FIX Algorithmic Trading Definition Language Online Specification — FIX Trading Community
• Staff Report on Algorithmic Trading in U.S. Capital Markets — Staff of the U.S. Securities and Exchange Commission
• Evidence boundary

The rest of the Schedule-Based Execution family#

• TWAP ExecutionSplits an order into equal slices across equal time buckets.
• Historical VWAP ExecutionDistributes an order according to a historical intraday volume profile — heavier at the open and close.
• Adaptive VWAP ExecutionRe-plans the remaining schedule from realised volume so far plus a forecast of what is left.