Basel IV Output Floor:
Recalibrating IRB Models for the New Capital Regime

Basel IV—formally the "finalisation of Basel III"—introduces the most significant change to bank capital regulation since the 2010 Basel III package. At its centre is the output floor: a constraint preventing banks on the Internal Ratings-Based (IRB) approach from holding capital more than 27.5% below what the Standardised Approach (SA) would require for the same portfolio. For banks with well-calibrated, conservative IRB models, the floor is binding on entire asset classes.

The Output Floor Mechanics

The output floor operates at the aggregate level. A bank computes its total RWA under the IRB approach (RWA_IRB), then computes the equivalent under the revised SA (RWA_SA). If RWA_IRB falls below 72.5% of RWA_SA, the bank must use the floored RWA for capital calculation:

The floor is phased in transitionally: 50% in 2025, 55% in 2026, 60% in 2027, 65% in 2028, 70% in 2029, reaching the final 72.5% in 2030. European jurisdictions implementing CRR3 follow this schedule; the UK's PRA has adopted a similar timeline under Basel 3.1.

IRB Risk Weight Formula

Under the IRB approach, the risk weight for a corporate or retail exposure is computed from the Vasicek single-factor model:

where R is the asset correlation (a function of PD, ranging from 12% to 24% for corporates), N is the standard normal CDF, G is its inverse, M is effective maturity, and b is the maturity adjustment. This formula produces capital consistent with a 99.9% confidence level over a 1-year horizon.

import numpy as np
from scipy.stats import norm
from dataclasses import dataclass

@dataclass
class Exposure:
    ead: float          # Exposure at Default (€)
    pd: float           # Probability of Default (decimal)
    lgd: float          # Loss Given Default (decimal)
    maturity: float     # Effective maturity (years)
    asset_class: str    # 'corporate', 'retail_mortgage', 'retail_other', 'sme'

def irb_rw_corporate(pd: float, lgd: float, maturity: float) -> float:
    """Basel IV Foundation IRB risk weight for corporate exposures."""
    pd = max(pd, 0.0003)   # PD floor: 0.03%
    R = 0.12 * (1 - np.exp(-50*pd))/(1 - np.exp(-50)) + \
        0.24 * (1 - (1 - np.exp(-50*pd))/(1 - np.exp(-50)))
    b = (0.11852 - 0.05478 * np.log(pd))**2
    ma = (1 + (maturity - 2.5) * b) / (1 - 1.5 * b)
    wcdr = norm.cdf((1-R)**(-0.5) * norm.ppf(pd)
                   + (R/(1-R))**0.5 * norm.ppf(0.999))
    rw = (lgd * wcdr - lgd * pd) * ma * 12.5 * 1.06
    return rw

def sa_rw_corporate(pd: float, secured_residential: bool = False) -> float:
    """Simplified Basel IV SA risk weight table (unrated corporate)."""
    if secured_residential:
        return 0.35
    if pd < 0.002:  return 0.65    # Investment-grade proxy
    if pd < 0.01:   return 0.85
    if pd < 0.05:   return 1.00
    return 1.50

def apply_output_floor(rwa_irb: float, rwa_sa: float,
                        floor_pct: float = 0.725) -> float:
    return max(rwa_irb, floor_pct * rwa_sa)

Impact by Portfolio Type

The floor's impact is highly heterogeneous. Retail mortgage portfolios, where IRB banks have historically achieved the lowest risk weights (often 10–15% for prime residential mortgages), face the largest relative increase. Corporate portfolios tend to be less affected because SA weights for unrated corporate exposures under the revised framework are lower than under Basel II.

Capital Ratio Sensitivity to PD Assumptions

Under the output floor, a bank's capital ratio becomes sensitive not only to its IRB PD estimates, but to the interaction between IRB and SA calculations. A PD upgrade (lower PD assumption) reduces IRB RWA but has no effect on SA RWA—and if the bank is already floor-constrained, the upgrade provides zero capital relief.

Transition and Model Recalibration Strategy

The SA Input Quality Problem

A counterintuitive implication of the output floor is that it creates incentives to improve SA inputs. If a bank can reduce its SA RWA by providing better collateral documentation, more accurate property valuations, or more precise counterparty data—then the SA floor is lower, and the bank gains capital relief even if its IRB models are unchanged.

This is particularly relevant for commercial real estate exposures, where the LTV-based SA risk weights under Basel IV are highly sensitive to the reported loan-to-value ratio. A portfolio with LTV below 60% qualifies for a 50% risk weight; above 80%, the risk weight doubles. Ensuring accurate, current property valuations has direct P&L implications under the new framework.