model_clo_insight.analysis.stats module

Statistical Module for Monte Carlo Default / Loss Distributions

Computes the rating-based cumulative default/loss hurdles, and diagnostic statistics at both the pool and loan level.

_solve_for_rho(a, b)

Solves for Vasicek correlation for a given mean and variance

Solves for rho within a Vasicek distribution such that the observed mean and variance are at the target

Parameters
Returns

rho single correlation parameter for a Vasicek distribution

Return type

float

_variance_func(x, y, z)

Used in correlation solver

Returns

variance for a Vasicek distribution

Return type

float

Notes

  • Uses Numpy multivariate normal distribution

calc_default_diagnostics(def_pct_matrix)

Computes the expected (exposure at default) per loan based on the simulation results

Parameters

def_pct_matrix (ndarray) – simulation results from model_clo_insight.engines.LGD.calc_def_pct_from_amort()

Returns

exposure at default per loan

Return type

ndarray

calc_rating_percentile(target_pd, loss_dist)

Computes Rating-Based Cumulative Default / Loss Thresholds

Parameters

  • target_pd (float) – target PD, based on idealized default table (IDT)

  • loss_dist (ndarray) – histogram computed from run_stats()

Returns

cumulative default / loss level at or around 1 - target_pd

Return type

float

Notes

  • Performs an interpolation as pool default/loss distributions can be lumpy

  • This algorithm was taken from the CLO Asset Model C# code: CalcStats() line 1319

interpolate_pd_func()

Creates an interpolation mapping function for the DBRSM IDT

Returns

pointer to the interpolation mapping function created in this method

Return type

function pointer

run_stats(monte_carlo_loss, securities, transaction, settings, methodology_params)

Computes all required statistical values for the simulation results. Last large calculation in the model

Parameters

  • monte_carlo_loss (ndarray) – raw simulation results

  • securities (list[clo_internal_objects.Corp_Loan]) – List of the loans in the pool

  • transaction (clo_internal_objects.TransactionData) – Data at the transaction (e.g. securitization) level:

  • settings (clo_internal_objects.ModelSettings) – settings object, e.g. monte carlo seed, number of trials

  • methodology_params – (clo_internal_objects.MethodologyParamsDefaults): methodology params w.r.t. the default simulation

Returns

results dict, histograms, cumulative default/loss hurdles, moments, diagnostics

Return type

dict

Note that an extra element is needed to ensure 100% defaults go into the 100% (not 99%) bucket Also note that we need to convert both the bins & data to float32 to avoid floating point errors when cumulative loss is exact size of a bin (important for lumpy pools)