---
title: "IRB defaults and explicit LGD treatment"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{IRB defaults and explicit LGD treatment}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

Default FIRB with supervisory LGD has zero K and EL equal to LGD times EAD.
Own-estimate AIRB and retail use positive LGD minus ELBE for K and ELBE for EL.
This corrects the default branch in version 1.2.0 (CRR Articles 153, 154, 158).

```{r}
library(riskweightedassets)
irb_capital_requirement(1, .4, .2, 2.5, defaulted = TRUE, elbe = .1,
                       lgd_treatment = "SUPERVISORY")
irb_capital_requirement(1, .4, .2, 2.5, defaulted = TRUE, elbe = .1,
                       lgd_treatment = "OWN_ESTIMATES")
```

For EAD 1,000,000 these give RWEA 0 / 3,750,000 and expected loss
400,000 / 100,000 respectively. Coverage 250,000 produces FIRB shortfall
150,000 and excess zero. The portfolio tests verify these values and their
own-funds and output-floor consequences in both reporting views.

Default calls require explicit lgd_treatment. Default normalises PD to one;
a PD of one without default is rejected. Portfolio output retains pd_input,
effective pd, defaulted and lgd_treatment. FIRB maps to SUPERVISORY;
AIRB (including supported retail) maps to OWN_ESTIMATES.
FIRB retail, unknown subclasses and unsupported approaches fail closed.
Slotting has no separate implementation and must not be sent through this formula.
The existing OTHER_RETAIL alias remains accepted by the direct correlation
helper; canonical portfolio retail subclass is RETAIL_OTHER.

Performing formulas, retail correlations and maturity-adjustment rules are
unchanged. Published reference inputs are unchanged, and historical output
snapshots must not be mistaken for acceptance results of the corrected version.