Credit analytics¶

The abaquant.credit namespace provides transition-matrix construction, bond-value distributions, CDS/CDO helpers, Gaussian-copula simulation, credit VaR/CVaR, and fundamentals-based proxy scoring.

Transition matrices¶

from abaquant.credit import build_transition_matrix, DEFAULT_TM

transition_matrix = build_transition_matrix(DEFAULT_TM)

A transition matrix stores conditional probabilities:

\[P_{ij}=\Pr(R_{t+1}=j\mid R_t=i).\]

Rows are starting rating states. Columns are destination states, including default where represented.

Bond values by rating¶

import numpy as np
from abaquant.credit import bond_values_per_rating

spreads = np.tile(np.linspace(0.01, 0.08, 5), (17, 1))
values = bond_values_per_rating(
    face_value=100.0,
    coupon_rate=0.05,
    T=5,
    payments_per_year=1,
    recovery_pct=0.40,
    spreads=spreads,
)

The valuation layer maps possible destination ratings to spread-adjusted bond values.

Portfolio distribution¶

from abaquant.credit import independent_distribution, expected_value_and_sigma

bonds_data = [
    {"name": "Bond A", "rating_idx": 0, "values": values},
    {"name": "Bond B", "rating_idx": 2, "values": values * 0.95},
]
distribution = independent_distribution(bonds_data, transition_matrix)
expected_values, moments = expected_value_and_sigma(bonds_data, transition_matrix)

Independent portfolio distributions are tractable for compact examples. They should not be treated as full credit portfolio models when defaults are materially correlated.

Gaussian copula simulation¶

import numpy as np
from abaquant.credit import gaussian_copula_simulation

corr = np.array([[1.0, 0.25], [0.25, 1.0]])
simulation = gaussian_copula_simulation(
    bonds_data,
    transition_matrix,
    corr,
    n_sims=10000,
    seed=42,
)

The one-factor latent-variable frame is:

\[X_i=\sqrt{\rho}Z+\sqrt{1-\rho}\epsilon_i.\]

Default occurs when \(X_i\) falls below the threshold implied by the default probability.

CDS valuation¶

from abaquant.credit import value_cds

cds = value_cds(
    hazard_rate=0.02,
    discount_rate=0.04,
    maturity=5,
    recovery_rate=0.40,
)
fair_spread = cds["spread"]

CDS valuation decomposes the contract into premium-leg and contingent-leg components.

CDO tranche valuation¶

import numpy as np
from abaquant.credit import gauss_hermite_normal, value_tranche

nodes, weights = gauss_hermite_normal(10)
tranche_value = value_tranche(
    hazard_rate=0.03,
    rho=0.25,
    n=20,
    recovery_rate=0.40,
    attachment=0.03,
    detachment=0.07,
    risk_free_rate=0.04,
    periods=np.arange(1.0, 6.0),
    factor_nodes=nodes,
    weights=weights,
)

Tranche valuation is very sensitive to correlation, recovery, default probability, and model form.

Fundamentals-based credit proxy scoring¶

from abaquant.credit import CreditAnalysisInputs, calculate_credit_proxy_metrics

assessment = calculate_credit_proxy_metrics(inputs)
score = assessment.synthetic_credit_proxy_score
band = assessment.synthetic_credit_proxy_band

Credit proxy scoring combines accounting, market-equity, and historical series inputs when available.

Common metrics include:

Metric	Meaning
Debt-to-equity	leverage relative to book equity.
Net debt to EBITDA	debt burden relative to operating earnings proxy.
Interest coverage	operating profit relative to interest expense.
Current ratio	short-term liquidity ratio.
Quick ratio	liquidity excluding inventory.
Altman-style Z score	blended accounting distress heuristic.
Piotroski-style F score	accounting quality and trend heuristic where enough data exist.
Synthetic proxy band	AbaQuant’s internal qualitative band from normalized metrics.

Scenario analysis¶

Credit proxy assessments can be stressed by changing debt, EBITDA, revenue, margins, cash, or market value assumptions. Use scenario analysis to identify which inputs dominate the synthetic score.

Interpretation limits¶

Credit proxy scoring is not an agency rating. It does not include covenant analysis, debt maturity schedules, collateral, legal seniority, sector-specific adjustments, liquidity backstops, qualitative management assessment, or forward-looking analyst judgment.