What's the Monte Carlo workflow for simulating credit portfolio losses?

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AcadiFi · Accepted Answer

A factor-based Monte Carlo credit simulation, similar to the CreditMetrics/KMV approach, follows this workflow: (1) Specify factor structure: each obligor's asset return A_i = sqrt(rho_i) * F + sqrt(1 - rho_i) * epsilon_i, where F is a common (or multi-factor) systematic factor, epsilon_i is idiosyncratic, both standard normal, and rho_i is asset correlation with the factor. (2) Set default threshold: obligor i defaults if A_i < Phi^-1(PD_i). For PD = 1.5%, threshold = -2.17. (3) Calibrate correlations: Basel IRB assigns correlations 12-24% by asset class; Merton-style models estimate from equity return correlations divided by (N(d1))^2. (4) Monte Carlo loop: for each of M = 200,000 paths: - Draw F from N(0,1) - Draw epsilon_i for each obligor - Compute A_i, compare to threshold, mark defaults - Sum losses: L = sum of EAD_i * LGD_i * 1(default) - Record L in distribution (5) Extract metrics: EL = mean(L), UL = std(L), VaR99 = 99th percentile of L, Expected Shortfall = mean(L | L > VaR99). Numerical illustration: 500-obligor portfolio, average EAD $2M, average PD 1.2%, average LGD 45%, rho = 0.18. Analytical EL = 500 * 2M * 0.012 * 0.45 = $5.4M. Simulated UL = $12.5M, VaR99 = $38M, ES99 = $52M. The ratio VaR99 / EL = 7.0 reflects fat tails from systematic factor exposure. ```mermaid flowchart TD A[Factor Model] --> B[Draw F
and epsilons] B --> C[Compute
asset returns] C --> D[Compare to
thresholds] D --> E[Aggregate
losses] E --> F[Next path] F --> B E --> G[VaR, ES] ``` Variance reduction via importance sampling and stratification on F cuts simulation time by 10-100x for tail measures.

What's the Monte Carlo workflow for simulating credit portfolio losses?

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