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| 1 | +# Model Risk Report |
| 2 | +## Integrated Risk App — Market & Credit Risk |
| 3 | + |
| 4 | +--- |
| 5 | + |
| 6 | +## 1. Model Purpose & Intended Use |
| 7 | + |
| 8 | +### Purpose |
| 9 | + |
| 10 | +The purpose of this model is to **measure and validate portfolio-level market and credit risk** using standard quantitative risk methodologies commonly employed by institutional investors, pensions, and risk management teams. |
| 11 | + |
| 12 | +The model is designed as a **validation sandbox**, emphasizing: |
| 13 | +- Transparent assumptions |
| 14 | +- Reproducible results |
| 15 | +- Clear separation between model logic and presentation |
| 16 | +- Standard backtesting diagnostics |
| 17 | + |
| 18 | +### Intended Use |
| 19 | + |
| 20 | +This model is intended for: |
| 21 | +- Risk measurement and monitoring |
| 22 | +- Model validation exercises |
| 23 | +- Educational and demonstrative analysis |
| 24 | + |
| 25 | +### Non-Intended Use |
| 26 | + |
| 27 | +The model is **not** intended for: |
| 28 | +- Trading or portfolio optimization |
| 29 | +- Real-time risk management |
| 30 | +- Regulatory capital calculation |
| 31 | +- Production deployment |
| 32 | + |
| 33 | +--- |
| 34 | + |
| 35 | +## 2. Data Description |
| 36 | + |
| 37 | +### Market Data |
| 38 | + |
| 39 | +- Asset returns are computed from historical price data |
| 40 | +- Data frequency: daily |
| 41 | +- Data source: publicly available market data (via `yfinance`, demo use only) |
| 42 | + |
| 43 | +Returns are computed as simple or log returns and aggregated into a portfolio using fixed user-defined weights. |
| 44 | + |
| 45 | +### Credit Data |
| 46 | + |
| 47 | +Credit risk inputs are provided as tabular datasets containing: |
| 48 | +- Probability of Default (PD) |
| 49 | +- Loss Given Default (LGD) |
| 50 | +- Exposure at Default (EAD) |
| 51 | + |
| 52 | +These inputs are assumed to be **exogenous** and are not estimated dynamically by the model. |
| 53 | + |
| 54 | +--- |
| 55 | + |
| 56 | +## 3. Methodology Overview |
| 57 | + |
| 58 | +### 3.1 Market Risk Measures |
| 59 | + |
| 60 | +All market risk measures follow a **loss-based convention**, where reported values represent **positive losses**. |
| 61 | + |
| 62 | +#### Value at Risk (VaR) |
| 63 | + |
| 64 | +VaR at confidence level α is defined as the loss threshold exceeded with probability: |
| 65 | + |
| 66 | +\[ |
| 67 | +P(L > \text{VaR}_\alpha) = 1 - \alpha |
| 68 | +\] |
| 69 | + |
| 70 | +#### Expected Shortfall (ES) |
| 71 | + |
| 72 | +Expected Shortfall is defined as the **average loss conditional on exceeding VaR**: |
| 73 | + |
| 74 | +\[ |
| 75 | +\text{ES}_\alpha = \mathbb{E}[L \mid L > \text{VaR}_\alpha] |
| 76 | +\] |
| 77 | + |
| 78 | +--- |
| 79 | + |
| 80 | +### 3.2 Market Risk Methodologies |
| 81 | + |
| 82 | +The following methodologies are implemented: |
| 83 | + |
| 84 | +#### Historical Simulation |
| 85 | +- Empirical quantiles of historical portfolio returns |
| 86 | +- No distributional assumptions |
| 87 | +- Assumes stationarity of historical returns |
| 88 | + |
| 89 | +#### Parametric (Normal) |
| 90 | +- Portfolio returns assumed normally distributed |
| 91 | +- Mean and covariance estimated from historical data |
| 92 | +- Closed-form VaR and ES expressions |
| 93 | + |
| 94 | +#### Monte Carlo Simulation |
| 95 | +- Multivariate normal simulation of asset returns |
| 96 | +- Mean and covariance estimated from data |
| 97 | +- Light covariance shrinkage applied for numerical stability |
| 98 | +- Portfolio losses simulated to estimate VaR and ES |
| 99 | + |
| 100 | +#### Filtered Historical Simulation (GARCH-lite) |
| 101 | +- Portfolio returns filtered using fixed-parameter GARCH(1,1) |
| 102 | +- Standardized residuals used for tail estimation |
| 103 | +- One-step-ahead volatility forecast applied |
| 104 | +- Captures time-varying volatility while retaining empirical tails |
| 105 | + |
| 106 | +--- |
| 107 | + |
| 108 | +### 3.3 Credit Risk Methodology |
| 109 | + |
| 110 | +Credit risk is measured using the **Expected Loss (EL)** framework: |
| 111 | + |
| 112 | +\[ |
| 113 | +\text{EL} = \text{PD} \times \text{LGD} \times \text{EAD} |
| 114 | +\] |
| 115 | + |
| 116 | +Expected Loss is: |
| 117 | +- Computed at the facility level |
| 118 | +- Aggregated to portfolio level |
| 119 | +- Decomposed by segment where applicable |
| 120 | + |
| 121 | +No default correlation or portfolio credit model (e.g. Vasicek) is assumed. |
| 122 | + |
| 123 | +--- |
| 124 | + |
| 125 | +## 4. Backtesting & Validation |
| 126 | + |
| 127 | +### 4.1 Market Risk Backtesting |
| 128 | + |
| 129 | +Market risk models are evaluated using **rolling out-of-sample backtests**. |
| 130 | + |
| 131 | +- 1-day VaR horizon |
| 132 | +- Rolling estimation window |
| 133 | +- VaR forecast computed using information available up to time *t−1* |
| 134 | +- Exceptions recorded when realized return breaches the VaR threshold |
| 135 | + |
| 136 | +--- |
| 137 | + |
| 138 | +### 4.2 Kupiec Proportion-of-Failures (POF) Test |
| 139 | + |
| 140 | +The Kupiec POF test evaluates **unconditional coverage** of the VaR model. |
| 141 | + |
| 142 | +#### Null Hypothesis |
| 143 | + |
| 144 | +\[ |
| 145 | +H_0: \pi = 1 - \alpha |
| 146 | +\] |
| 147 | + |
| 148 | +Where: |
| 149 | +- π is the observed exception rate |
| 150 | +- α is the VaR confidence level |
| 151 | + |
| 152 | +#### Test Statistic |
| 153 | + |
| 154 | +The likelihood ratio statistic follows an asymptotic χ²(1) distribution. |
| 155 | + |
| 156 | +- High LR statistic / low p-value → reject model coverage |
| 157 | +- Low LR statistic → model consistent with expected exception rate |
| 158 | + |
| 159 | +--- |
| 160 | + |
| 161 | +## 5. Model Assumptions & Limitations |
| 162 | + |
| 163 | +### Key Assumptions |
| 164 | + |
| 165 | +- Historical returns are representative of future risk |
| 166 | +- Portfolio weights are static over the risk horizon |
| 167 | +- Normality assumptions apply where specified |
| 168 | +- Credit risk inputs (PD, LGD, EAD) are externally provided |
| 169 | + |
| 170 | +### Limitations |
| 171 | + |
| 172 | +- No dynamic correlation modeling |
| 173 | +- No intraday or high-frequency data |
| 174 | +- No regulatory capital framework (e.g. Basel) implemented |
| 175 | +- GARCH parameters are fixed rather than estimated |
| 176 | + |
| 177 | +These limitations are **intentional** to preserve clarity and interpretability. |
| 178 | + |
| 179 | +--- |
| 180 | + |
| 181 | +## 6. Model Governance Notes |
| 182 | + |
| 183 | +- Model logic is isolated in `risklib/` |
| 184 | +- Configuration objects explicitly capture modeling assumptions |
| 185 | +- UI layer does not modify or implement risk calculations |
| 186 | +- Backtesting is performed out-of-sample |
| 187 | +- Results are reproducible and exportable |
| 188 | + |
| 189 | +This structure mirrors common **model risk governance principles**, including: |
| 190 | +- Transparency |
| 191 | +- Auditability |
| 192 | +- Separation of concerns |
| 193 | +- Clear documentation of assumptions |
| 194 | + |
| 195 | +--- |
| 196 | + |
| 197 | +## 7. Conclusion |
| 198 | + |
| 199 | +This model provides a **validation-focused implementation** of standard market and credit risk methodologies. |
| 200 | + |
| 201 | +The emphasis is on: |
| 202 | +- Correct methodology |
| 203 | +- Proper validation |
| 204 | +- Interpretability |
| 205 | +- Governance-aligned design |
| 206 | + |
| 207 | +The model is suitable as a **demonstration artifact** for risk analytics, model validation, and institutional risk roles. |
| 208 | + |
| 209 | +--- |
| 210 | + |
| 211 | +**End of Report** |
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