How does the Internal Models Approach (IMA) for market risk capital work under the FRTB framework?

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AcadiFi · Accepted Answer

The **Internal Models Approach (IMA)** under the Fundamental Review of the Trading Book (FRTB) is Basel's revised framework for calculating market risk capital using a bank's own models. It replaces the pre-FRTB IMA that was based on VaR and stressed VaR.

**IMA Capital Components**

The total IMA capital charge has three additive components:

**IMA Capital = ES Component + Default Risk Charge (DRC) + Stressed Capital Add-On (SES)**

| Component | What It Captures | Methodology |
|---|---|---|
| **Expected Shortfall (ES)** | General market risk across all risk factors | 97.5% ES with varying liquidity horizons |
| **Default Risk Charge (DRC)** | Jump-to-default risk for credit positions | Separate default simulation model (99.9%, 1-year) |
| **Stressed Capital Add-On (SES)** | Non-modellable risk factors | Stressed calibration for risk factors that fail data sufficiency tests |

**ES Component — Liquidity Horizons**

A major FRTB innovation: different risk factors have different **liquidity horizons** based on how quickly positions can be closed:

| Risk Factor Category | Liquidity Horizon |
|---|---|
| Large-cap equity prices | 10 days |
| Government bond yields (G7) | 20 days |
| Corporate credit spreads (IG) | 40 days |
| Small-cap equity volatilities | 60 days |
| Exotic credit correlations | 120 days |

The ES is computed as a composite across all five liquidity horizons, ensuring that illiquid risk factors contribute more to capital.

```mermaid
flowchart TD
    A["IMA Capital Charge"] --> B["ES Component"]
    A --> C["Default Risk Charge"]
    A --> D["Stressed Capital Add-On"]
    B --> E["Liquidity horizons: 10/20/40/60/120 days"]
    B --> F["Calibrated to stressed period"]
    C --> G["99.9% 1-year JTD simulation"]
    D --> H["Non-modellable risk factors at stressed levels"]
```

**Desk-Level Approval (Trading Desk Eligibility)**

Under FRTB, IMA approval is granted at the **individual trading desk level**, not bank-wide:

1. Each desk must pass **backtesting** (comparing model predictions to actual P&L)
2. Each desk must pass a **P&L attribution test** (model P&L must explain actual P&L)
3. Desks that fail either test are moved to the **Standardized Approach** (SA)

**Backtesting Zones:**

| Exceptions (250 days) | Zone | Consequence |
|---|---|---|
| 0-4 | Green | IMA continues |
| 5-9 | Yellow | Capital multiplier increases |
| 10+ | Red | Desk reverts to Standardized Approach |

**Worked Example**

Summerfield Securities has three trading desks:

| Desk | Backtesting | P&L Attribution | Approach |
|---|---|---|---|
| Rates | 3 exceptions (green) | Pass | IMA |
| Credit | 6 exceptions (yellow) | Pass | IMA (with higher multiplier) |
| Exotics | 11 exceptions (red) | Fail | **Standardized Approach** |

The exotics desk must calculate capital under the more conservative SA, while rates and credit desks benefit from IMA.

**Key Exam Points:**
- FRTB ES uses 97.5% confidence (not 99% as in old VaR)
- Liquidity horizons are a new and testable concept
- Desk-level approval is a fundamental change from the old bank-wide IMA

For more on FRTB, explore our FRM Part II materials.

How does the Internal Models Approach (IMA) for market risk capital work under the FRTB framework?

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