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Credit — a method on inputs that do not exist#

Capstone · Actuarial

Source: Credit.hb · CreditAgent.ha · CreditTests.cs

Read this first#

houses.csv records sales, not mortgages. It has no loan-to-value, no interest rate, no borrower, and no default outcomes. So every input to this model is invented, and so is every coefficient:

  • the loan-to-value and the rate are synthesised, deterministically, from the sale price and a fixed seed;
  • the hazard coefficients are declared, not fitted — there are no defaults to fit them to;
  • the recovery on foreclosure is a declared 75% of the sale price.

This agent's number demonstrates a method. It measures nothing. It says nothing about any real borrower, and nothing in this repository may present it as though it did.

That warning is in three places — the top of Credit.hb, this page, and the program's output every time the credit agent reports — because one is too easy to miss.

Why the sample exists anyway#

Because a credit view is a real part of a purchase decision, and the question of how it enters — as an agent that can veto the other two — is worth showing. A proportional-hazards model over loan attributes is worth showing too. Showing both on invented inputs is honest as long as nobody pretends otherwise.

The rule this repository follows: a number is a measurement or it is a demonstration, and which one it is must never be ambiguous.

The synthesis#

def scatter01(price, seed) ≔ (price · 0.000037 + seed · 0.61) − floor(price · 0.000037 + seed · 0.61)

fn loanToValueOf(price, seed) ↦ 0.60 + 0.35 · scatter01(price, seed)
fn rateOf(price, seed)        ↦ 0.03 + 0.05 · scatter01(price, seed + 1)

The fractional part of a fixed affine map: a number in [0, 1) that depends only on price and seed. Not random, and not pretending to be. A fixed seed makes the invented loan reproducible, so it can be tested, and means nobody can mistake variation between runs for signal.

The hazard#

fn defaultHazard(x, b) ↦ hazardOf(x, b)
fn defaultChance(h)    ↦ 1 − exp(0 − h)

hazardOf is Cox's proportional hazards from Prelude.Sequences: exp(x · b), clamped. With the declared coefficients [4, 20, −6] over [loan-to-value, rate, 1], borrowing more of the price and paying more interest both raise the hazard. That is a property of the numbers chosen, and the test says so rather than implying the data showed it.

What the tests check — exactly two things#

  1. The synthesis is deterministic — the same price and seed give the same loan every run — and it depends on the price, so a synthesis that returned a constant could not pass.
  2. The arithmetic is what the formulas say — every value computed independently to five or six decimals.

Nothing more is tested, because nothing more is true.

A Hilbert defect found here, and fixed#

scatter01 is a def. It was first written as a fn, and the Hilbert compiler accepted that without a word — then the generated C# failed to build, with the call routed to System.Math.Scatter01, as though a sibling function were a built-in like floor. Hilbert now inlines a sibling fn as it does a def. The helper stays a def because nothing outside this file calls it, which is how the Prelude is written throughout. See diagnostics.