fintech-algorithms
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Implementation-Shortfall Execution

Install and import#

bash
npm install fintech-algorithms
ts
import { implementationShortfallExecution } from "fintech-algorithms/execution-and-transaction-cost-analysis/cost-risk-optimization/implementation-shortfall-execution";

Signature#

implementationShortfallExecution(input)

Minimises total shortfall against the arrival price, including the opportunity cost of quantity that never executes. Unexecuted quantity is a real cost, and a strategy measured only on filled shares hides it.

Parameters#

NameTypeNotes
inputShortfallInputArrival price, quantity, impact and volatility parameters, and the urgency that trades impact against timing risk.

Returns#

{ schedule, expected_shortfall_bps, market_impact, timing_risk, opportunity_cost, … }

Shortfall decomposed into impact, timing risk and opportunity cost — the decomposition is what makes it actionable.

Errors#

  • When the arrival price is not positive — throws

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

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#

input
{
  "remaining_quantity": 10000,
  "side": "buy",
  "decision_price_atoms": 1000000,
  "current_price_atoms": 1001000,
  "spread_bps": 4,
  "impact_coefficient_bps": 35,
  "average_daily_volume": 1000000,
  "volatility_bps": 18,
  "risk_aversion": 0.8,
  "urgency_bps": 12,
  "intervals_remaining": 8,
  "max_child_quantity": 3000,
  "candidate_step_quantity": 500,
  "lot_size": 100
}

Call#

implementationShortfallExecution(input)

Returns#

object with 14 fields: side, decision_price_atoms, current_price_atoms, signed_move_bps, adverse_move_bps, remaining_quantity, selected_child_quantity, post_child_quantity, …

{
  "side": "buy",
  "decision_price_atoms": 1000000,
  "current_price_atoms": 1001000,
  "signed_move_bps": 10,
  "adverse_move_bps": 10,
  "remaining_quantity": 10000,
  "selected_child_quantity": 3000,
  "post_child_quantity": 7000,
  "selected_total_score": 122453.181772,
  "selected_immediate_cost_score": 6315,
  "selected_opportunity_cost_score": 80500,
  "selected_inventory_risk_score": 35638.181772,
  "candidates": [
    {
      "child_quantity": 0,
      "residual_quantity": 10000,
      "immediate_cost_score": 0,
      "opportunity_cost_score": 115000,
      "inventory_risk_score": 50911.688245,
      "total_score": 165911.688245
    },
    {
      "child_quantity": 500,
      "residual_quantity": 9500,
      "immediate_cost_score": 1008.75,
      "opportunity_cost_score": 109250,
      "inventory_risk_score": 48366.103833,
      "total_score": 158624.853833
    },
    {
      "child_quantity": 1000,
      "residual_quantity": 9000,
      "immediate_cost_score": 2035,
      "opportunity_cost_score": 103500,
      "inventory_risk_score": 45820.519421,
      "total_score": 151355.519421
    }
  ],
  "state": "execute-now"
}

Other exports#

This module also exports almgrenChrissOptimalExecution, arrivalPriceExecution, liquiditySeekingExecution, opportunisticDarkPoolExecution, 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#

Implementation-Shortfall Execution — system map

Calculation flow#

Implementation-Shortfall Execution calculation flow 
flowchart LR
    S1["Validate side prices parent candidates lots and score "]
    S2["Compute sideaware move from decision price and retain "]
    S3["Score each declared child candidate"]
    S4["Choose the minimum score with deterministic smallerchi"]
    S1 --> S2
    S2 --> S3
    S3 --> S4
    S4 --> D{"current price exactly equal to the decision price"}
    D --> O["selected_child_quantity + diagnostics"]
    O --> A["Audit: Selected child belongs to the candidate set and does not e"]

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#

The rest of the Cost/Risk Optimization family#