Point-in-Time PD

Install and import#

npm install fintech-algorithms

import { pointInTimePd } from "fintech-algorithms/credit-risk-and-default/probability-of-default/point-in-time-pd";

Signature#

pointInTimePd(through_the_cycle_pd_value, borrower_log_odds_shift, macro_factor_z, macro_sensitivity, alert_threshold)

Overlays a borrower-specific shift and a macro shift on the log-odds of a through-the-cycle default probability, returning the resulting point-in-time probability and the size of each shift.

Parameters#

Returns#

{ through_the_cycle_pd: number; baseline_log_odds: number; borrower_log_odds_shift: number; macro_log_odds_shift: number; point_in_time_pd: number; cycle_uplift: number; alert_threshold: number; state: string; reason: string }

baseline_log_odds is the log-odds of the supplied long-run probability and macro_log_odds_shift is sensitivity times factor. point_in_time_pd is the logistic transform of the baseline plus both shifts, and cycle_uplift is that probability minus the long-run one. state is at-or-above-alert or below-alert, and reason records that this overlay is a declared package convention rather than a universal regulatory or accounting formula.

Errors#

• When any argument is not a finite number — throws Error
• When through_the_cycle_pd_value or alert_threshold is not strictly between zero and one — throws Error
• When macro_sensitivity is negative — throws Error

Complexity: time O(1), space O(1).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

0.03

0.25

0.8

0.55

0.06

Call#

pointInTimePd(through_the_cycle_pd_value, borrower_log_odds_shift, macro_factor_z, macro_sensitivity, alert_threshold)

Returns#

object with 9 fields: through_the_cycle_pd, baseline_log_odds, borrower_log_odds_shift, macro_log_odds_shift, point_in_time_pd, cycle_uplift, alert_threshold, state, …

{
  "through_the_cycle_pd": 0.03,
  "baseline_log_odds": -3.476098689835,
  "borrower_log_odds_shift": 0.25,
  "macro_log_odds_shift": 0.44,
  "point_in_time_pd": 0.058080015587,
  "cycle_uplift": 0.028080015587,
  "alert_threshold": 0.06,
  "state": "below-alert",
  "reason": "declared-log-odds-overlay-not-universal-ifrs-or-regulatory-formula"
}

Other exports#

This module also exports logisticPdModel, probitPdModel, throughTheCyclePd, mertonDistanceToDefault, campbellHilscherSzilagyiDistressProbability, bharathShumwayNaiveDistanceToDefault, 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["Freeze target horizon TTC anchor scenario vintage and "]
    S2["Convert TTC PD to baseline logodds"]
    S3["Calculate borrower and macro shifts separately"]
    S4["Add shifts and apply a stable sigmoid"]
    S5["Return PIT PD uplift contributions threshold state and"]
    S1 --> S2
    S2 --> S3
    S3 --> S4
    S4 --> S5
    S5 --> D{"the TTC anchor must lie strictly inside 01 and scenario di"}
    D --> O["point_in_time_pd + diagnostics"]
    O --> A["Audit: macrofactorz  0 and borrower shift  0 reproduces TTC PD"]

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#

• A survey of cyclical effects in credit risk measurement models — Linda Allen and Anthony Saunders
• IFRS 9 Financial Instruments — International Accounting Standards Board
• IRB approach: minimum requirements to use IRB approach — Basel Committee on Banking Supervision
• Supervisory Guidance on Model Risk Management — OCC, Board of Governors of the Federal Reserve System, and FDIC
• Evidence boundary

The rest of the Probability of Default family#

• Logistic PD ModelApplies a logistic link to a supplied linear credit score and reports the resulting default probability alongside the per-featu…
• Probit PD ModelApplies the standard normal cumulative distribution to a supplied linear latent score and reports the resulting default probabi…
• Through-the-Cycle PDTurns a multi-year history of obligor counts and default counts into annual default rates, averages them into a through-the-cyc…
• Merton Distance-to-DefaultSolves the two-equation Merton system iteratively for the unobserved asset value and asset volatility implied by observed equit…
• Campbell-Hilscher-Szilagyi Distress ProbabilityEvaluates the published Campbell, Hilscher and Szilagyi twelve-month-lag logit with its eight accounting and market inputs, ret…
• Bharath-Shumway Naive Distance-to-DefaultComputes the Bharath and Shumway naive distance to default, which approximates the Merton solve with closed-form substitutes fo…