Portfolio & Simulation Parameters
CreditMetrics Engine| Name | Rating | Face ($M) | Cpn (%) | Mat (Y) | Rec (%) | Del |
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CreditMetrics Mathematical Architecture
1. Latent Asset Return & Transition Thresholds:
$$Z_i \sim \mathcal{N}(0, 1), \quad Z_{i, s} = \Phi^{-1}\left(\sum_{m=s+1}^8 P_{i, m}\right)$$Obligor $i$ ends in rating state $s$ if $Z_{i, s} < Z_i \le Z_{i, s-1}$.
2. Forward Bond Revaluation:
$$V_{i, s} = \sum_{\tau=1}^{T_i - 1} \frac{C_i}{(1 + f_{s, \tau})^\tau} + \frac{F_i + C_i}{(1 + f_{s, T_i - 1})^{T_i - 1}}, \quad V_{i, D} = F_i \cdot R_i$$3. Analytical Portfolio Volatility:
$$\sigma_{\text{port}} = \sqrt{\sum_i \sigma_i^2 + 2 \sum_{i < j} \text{Cov}(V_i, V_j)}$$where $\text{Cov}(V_i, V_j)$ is computed via bivariate normal integrals $\Phi_2(Z_{i, s}, Z_{j, s'}; \rho)$.
4. CreditVaR & Expected Shortfall:
$$\text{CreditVaR}_\alpha = \mathbb{E}[V] - q_{1-\alpha}(V_{\text{port}})$$ $$\text{CVaR}_\alpha = \mathbb{E}[\text{Loss} \mid \text{Loss} \ge \text{CreditVaR}_\alpha]$$Notice the characteristic fat right tail and positive skewness. Yellow bars denote losses between 95% and 99% VaR; red bars highlight the extreme 99% tail losses.
Scatter of simulated joint standardized asset returns for Obligor 1 and Obligor 2. Higher correlation aligns points along the 45-degree diagonal, driving concurrent downgrades and defaults.
Decomposition of portfolio risk across obligors comparing Notional Face Value, Standalone 99% VaR, and actual Component CreditVaR (marginal covariance contribution).
Obligor Risk Decomposition & Revaluation Profile
1-Year Horizon| Obligor | Rating | Face | Coupon | Mat | Expected Val | Volatility ($\sigma_i$) | Standalone VaR | Component VaR (%) |
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Portfolio Sensitivity Analysis (Dual 5x5 Heatmaps)
Correlation ($\rho$) vs Concentration on 99% CreditVaR ($M)
| $\rho \downarrow$ \ Portfolio $\rightarrow$ | Equal | Top-Heavy | Bipolar | HY-Heavy | Base |
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Base Rating vs Recovery Rate on Credit Volatility ($\sigma_{\text{Credit}}$)
| Rating $\downarrow$ \ Rec % $\rightarrow$ | 20% | 30% | 40% | 50% | 60% |
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