pyAssetCorr 0.1.2

Estimate asset correlation from historical default data under the Vasicek credit-portfolio model.

pyAssetCorr

Estimate asset correlation from historical default data under the Vasicek credit-portfolio model.

A clean-room Python implementation of the most-used functionality of the R package AssetCorr: method-of-moments and maximum-likelihood estimators for intra- and inter-cohort asset correlation, with standard errors, information criteria, likelihood-ratio tests, and tools for overlapping multi-year cohorts.

See docs/USER_GUIDE.md for the full guide.

Why asset correlation?

In the Vasicek single-factor model an obligor's latent asset return is

A = sqrt(rho) * X + sqrt(1 - rho) * eps

with a systematic factor X shared across obligors and idiosyncratic eps. The obligor defaults when A falls below Phi^{-1}(PD). The asset correlation rho controls how strongly defaults cluster: it drives the tail of the portfolio loss distribution and hence economic and regulatory capital. pyAssetCorr estimates rho (and, for several cohorts, the inter-cohort coupling) from observed default-count time series.

Installation

pip install pyAssetCorr            # numpy + scipy only

From a checkout:

pip install -e ".[dev]"            # editable install with pytest

Requires Python >= 3.9. All computation is vectorized NumPy/SciPy — no compiled extensions or JIT needed. (An [accel] extra installs numba for an internal alternative kernel, but the built-in estimators run pure NumPy and do not use it, so it changes neither results nor speed.)

Quickstart

Data are two equal-length arrays: d = defaults per period, n = obligors per period.

import numpy as np
from pyassetcorr import intra_fmm, intra_mle, simulate_default_series

# Simulate a 10-year history with rho = 0.15, PD = 3%, 2000 obligors/year.
d, n = simulate_default_series(rho=0.15, pd=0.03, n=2000, T=10, seed=0)

# Method of moments (finite-sample corrected) with a confidence interval.
mom = intra_fmm(d, n, ci=True)
print(mom)                 # MomentResult(method='fmm', rho=..., se=..., ...)
print(mom.rho, mom.ci)

# Maximum likelihood, jointly estimating PD, with AIC/BIC and SE.
mle = intra_mle(d, n, pd="joint", ci=True)
print(mle.params["rho"], mle.params["pd"])
print(mle.aic, mle.bic, mle.se["rho"])

# The MLE integral is adaptive; pass `nodes` to check quadrature convergence,
# e.g. intra_mle(d, n, nodes=64). See the User Guide, "Checking quadrature
# convergence".

Several cohorts at once

from pyassetcorr import multi_cohort_mle, lr_test, multi_cohort_single_factor

# d, n are now (T x K): T periods, K cohorts.
fit = multi_cohort_mle(d_mat, n_mat)          # per-cohort rho + free gamma
print(fit.params["rho"], fit.params["gamma"])
print(fit.inter_corr)                          # inter-cohort asset-corr matrix

# Is a single common factor (gamma = 1) enough?
restricted = multi_cohort_single_factor(d_mat, n_mat)
print(lr_test(fit, restricted))                # likelihood-ratio test

The multi-cohort model nests cohorts under a single global factor Z plus per-cohort factors w_k, controlled by one coupling parameter gamma: intra-cohort correlation stays rho_k, inter-cohort correlation is gamma * sqrt(rho_i * rho_j). gamma = 1 is a single common factor, gamma = 0 independent cohorts.

Overlapping multi-year cohorts

Annual cohorts measured over an h-year horizon share calendar shocks, so the default series is autocorrelated and naive standard errors are too small. Use a HAC lag or non-overlapping subsample averaging:

from pyassetcorr import intra_fmm, group_average

intra_fmm(d, n, lag=h - 1)        # autocorrelation-robust (Frei-Wunsch) SE
group_average(d, n, horizon=h)    # average over non-overlapping subsamples

Estimators

Function	Kind	Description
intra_amm	MoM	Asymptotic method of moments (Gordy 2000)
intra_fmm	MoM	Finite-sample corrected method of moments
intra_jdp1	MoM	Unbiased joint-default-probability matching (Lucas 1995)
intra_jdp2	MoM	Biased JDP matching (literature parity)
intra_mle	MLE	Single-cohort Vasicek-Binomial MLE
multi_cohort_mle	MLE	Generalized multi-cohort MLE (nested two-level factor)

AssetCorr-style aliases (intraAMM, intraFMM, intraJDP1, intraJDP2, intraMLE) are provided for discoverability.

License

MIT. This is a clean-room implementation written from the published equations (see references below), not a translation of the GPL-3 R source, so it is free to use in both academic and commercial/financial settings.

References

• Vasicek, O. (2002). The Distribution of Loan Portfolio Value. Risk.
• Gordy, M. (2000). A comparative anatomy of credit risk models. J. Banking & Finance.
• Lucas, D. (1995). Default correlation and credit analysis. J. Fixed Income.
• Gordy, M. & Heitfield, E. (2010). Small-sample estimation of models of portfolio credit risk.
• Duellmann, K. & Gehde-Trapp, M. (2004). Probability of default estimation.
• Bluhm, C. & Overbeck, L. (2003). Systematic risk in homogeneous credit portfolios.
• Frei, C. & Wunsch, M. (2018). Moment Estimators for Autocorrelated Time Series and Default Correlations. J. Credit Risk.