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SHARC: SHAP-Based Interpretability in Machine Learning Risk Models for Regulatory Capital under ICAAP and CCAR

This paper introduces SHARC, a SHAP-based explainability framework that resolves the "black box" barrier for non-parametric machine learning models in regulatory capital estimation by decomposing stressed Value-at-Risk outputs into auditable components, thereby ensuring compliance with ICAAP and CCAR transparency requirements.

Original authors: Ujjwala Vadrevu

Published 2026-07-08

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ujjwala Vadrevu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a bank trying to figure out how much money it needs to keep in a safety vault to survive a financial disaster. In the past, banks used simple, transparent math formulas to do this. Everyone could see exactly how the formula worked, like looking at a clear glass box.

But recently, banks started using powerful, complex computer brains (Machine Learning) to predict disasters. These are more accurate, but they are like black boxes: you put a problem in, and a number comes out, but no one can see why the computer decided on that specific number. Regulators (the "police" of the financial world) hate this. They won't let banks use these black boxes because they can't audit the logic.

This paper introduces a solution called SHARC (SHAP for Regulatory Capital). Think of SHARC as a magic X-ray machine that can look inside the black box and show you exactly how the computer made its decision.

Here is how the paper breaks it down, using simple analogies:

1. The Problem: The "Black Box" vs. The "Glass Box"

The Old Way (Glass Box): Imagine a recipe where you can see every ingredient and exactly how much of it is used. If the cake tastes bad, you know it's because you added too much salt.
The New Way (Black Box): Imagine a robot chef that makes a perfect cake, but it mixes ingredients in a way no human can understand. The regulators say, "We can't let you use this robot unless you can explain why the cake tastes the way it does."
The Paper's Goal: The authors want to prove that their advanced robot chef (called a Gaussian Process Regression model) can be explained using SHARC, so regulators will finally let banks use it.

2. The Solution: The "Magic X-Ray" (SHARC)

The authors use a tool called SHAP (which stands for SHapley Additive exPlanations). Think of SHAP as a fair accountant from a game theory board game.

Imagine a group of friends (the data inputs) working together to win a prize (the final risk number).
The "fair accountant" (SHAP) looks at every possible way the friends could have worked together and calculates exactly how much each friend contributed to the win.
SHARC is just this accountant applied specifically to bank capital rules. It breaks down the final "Safety Vault Number" into tiny pieces and says: "This 1% came from the war in West Asia, this 0.5% came from climate change fears, and this 0.2% came from the AI bubble."

3. The Experiment: Three Disaster Scenarios

To test if their X-ray works, the authors simulated three different "apocalypse" scenarios:

West Asia War: A conflict causing markets to crash.
Climate Risk: Environmental disasters hitting specific regions.
AI Bubble: A tech crash where AI companies lose value.

They fed these scenarios into their complex robot model and then used SHARC to see what the model was thinking.

4. The Big Discovery: "The Trigger vs. The Stage"

The most important finding of the paper is a surprise about what actually drives the bank's risk number during a disaster.

The Old Belief: People thought that during a crisis, the Volatility (how shaky and unpredictable the market is) is the main driver of risk. It's like thinking the size of the storm is what scares you the most.
The SHARC Finding: The paper found that during a real, severe crash, the Directional Loss (how far the market actually falls) is the main driver. The volatility is just the background noise; the falling itself is what matters.
The Analogy: Imagine you are on a rollercoaster.
- Volatility is how much the car is shaking and rattling.
- Directional Loss is the car actually plummeting off a cliff.
- The paper says: "When you are plummeting off a cliff, the shaking (volatility) doesn't matter as much as the fact that you are falling (directional loss)."
- Why this matters: If a bank wants to lower its risk, it shouldn't just try to calm the shaking (buying insurance against volatility); it needs to get off the rollercoaster (reduce the position that is falling).

5. The Result: A Clear Report Card

The paper shows that SHARC can take a complex, scary number (like "We need $2.2 billion in capital") and break it down into a simple list that a regulator can read.

It proves that the "Black Box" isn't actually black; it's just hard to see without the right glasses.
It shows that the model is honest: if the scenario says "Europe crashes," the model says "Europe crashed," and SHARC proves it.
It creates a Force Plot (a visual chart) that acts like a receipt, showing exactly where every penny of risk came from.

Summary

This paper says: "We built a super-smart, complex computer model to predict financial disasters. Regulators were scared because they couldn't understand it. We used a tool called SHARC to take an X-ray of the model. We found that the model works perfectly, it follows the rules, and it tells us that during a crash, the size of the drop matters more than the shaking. Now, the regulators can see the logic, and banks can use this smarter model to keep the financial system safe."

Technical Summary: SHARC – SHAP-Based Interpretability in Machine Learning Risk Models for Regulatory Capital

1. Problem Statement

The adoption of non-parametric machine learning models, specifically Gaussian Process Regression (GPR), in regulatory capital estimation (ICAAP and CCAR) faces a fundamental governance barrier: the "black box" problem. While GPR and related architectures demonstrate predictive superiority over traditional parametric approaches (e.g., GARCH, Historical Simulation), their outputs lack analytical decomposability. Regulatory frameworks such as the Fundamental Review of the Trading Book (FRTB), ICAAP Pillar 2, and CCAR require models to be auditable, meaning capital estimates must be decomposable into underlying risk drivers that non-technical supervisors can interrogate. Traditional models satisfy this by construction; GPR does not, as its posterior predictive distribution is an integral over admissible functions, rendering the attribution of specific inputs to outputs non-trivial and non-linear. This paper addresses the need to resolve this transparency barrier without sacrificing the predictive accuracy of advanced ML architectures.

2. Methodology: The SHARC Framework

The paper introduces SHARC (SHAP for Regulatory Capital), a structured explainability framework that applies SHapley Additive exPlanations (SHAP) to the Hybrid GPR-HS architecture.

2.1 Theoretical Foundation

SHARC leverages SHAP, a model-agnostic method derived from cooperative game theory (Shapley, 1953; Lundberg & Lee, 2017). The framework relies on four axiomatic properties that map directly to regulatory audit requirements:

Local Accuracy: The sum of SHAP values equals the model output, ensuring complete decomposition of capital (no unexplained "phantom" capital).
Missingness: Features with zero input contribute zero to the output, preventing phantom attribution.
Consistency: If a feature's marginal contribution increases, its SHAP value cannot decrease, ensuring monotonicity.
Efficiency: The decomposition sums exactly to the difference between the model output and the baseline, ensuring zero residual.

2.2 Application to Stressed Value-at-Risk (SVaR)

The framework is applied to Stressed Value-at-Risk (SVaR) rather than base-case VaR, as SVaR represents the capital-binding regulatory measure. The methodology treats the SVaR calculation function $f(\mu, \sigma)$ as the target to be explained.

Input Features: The analysis utilizes $2N$ features derived from $N$ stressed GPR models: $N$ predicted conditional means ( $\mu_i$ ) and $N$ predicted conditional standard deviations ( $\sigma_i$ ) for portfolio assets.
Decomposition Formula: The SHARC framework formalizes the decomposition as:
$SVaR_{SHARC} = \phi_0 + \sum_{i} (\phi_{\mu_i} + \phi_{\sigma_i})$
Where $\phi_0$ is the baseline capital (pre-stress Day 1 SVaR), $\phi_{\mu_i}$ is the contribution of the directional mean (loss magnitude), and $\phi_{\sigma_i}$ is the contribution of the variance (volatility).
Implementation: Kernel SHAP is used due to its model-agnostic nature, treating the GPR posterior as a black box and estimating values via weighted linear regression over perturbed input coalitions. The analysis focuses on local interpretation (point-in-time outputs at $T=252$ ) to satisfy regulatory requirements for specific capital calculations, rather than global average behavior.

2.3 Scenario Testing

The framework is validated across three distinct macro stress scenarios:

West Asia War: Characterized by deep shocks to European and Hong Kong markets.
Climate Risk: Characterized by heterogeneous geographic shock concentrations.
AI Bubble/Regulatory Burden: Characterized by deep shocks to the US technology sector (S&P 500).

3. Key Results

3.1 Framework Fidelity and Traceability

The SHARC decomposition consistently maps SVaR outputs to the underlying scenario design. In the West Asia War scenario, the EURO STOXX 50 mean component (driven by a -40% shock) emerged as the primary driver, while indices with moderate shocks (FTSE 100, Nikkei 225) acted as mitigating components. Similarly, in the AI Bubble scenario, the S&P 500 mean component dominated due to the -45% tech sector shock. This confirms that the Hybrid GPR-HS architecture faithfully transmits scenario inputs through its non-linear structure, and SHARC renders this transmission transparent.

3.2 The Dominance of Mean over Variance Under Stress

The paper's primary analytical finding is the non-linear risk decomposition pattern observed under stress conditions:

Normal Conditions: Variance (volatility) typically drives VaR/ES calculations, consistent with theoretical literature (McNeil et al., 2015).
Stress Conditions: Under strong stress conditioning (e.g., a mandated -40% loss over 252 days), the mean return component (directional loss magnitude) consistently dominates the variance component in determining the final SVaR.
Mechanism: When a scenario dictates extreme negative directional losses, the implied daily mean return becomes deeply negative, acting as the binding constraint on capital. The variance component, while present, becomes secondary.

3.3 Regulatory Documentation Artifacts

The SHAP Force Plot is identified as a critical regulatory output. It provides a visual, zero-remainder decomposition of a specific terminal SVaR (e.g., -2.2231% for West Asia War) into baseline, mean-driven, and variance-driven components. This allows regulators to immediately identify which index exposures drive capital requirements and by how much, satisfying FRTB and ICAAP documentation standards.

4. Significance and Contributions

The paper claims four primary contributions that resolve the regulatory barrier to GPR adoption:

Axiomatic Regulatory Mapping: It formally maps SHAP's four axioms to FRTB, ICAAP, and CCAR documentation requirements, establishing SHAP as a theoretically grounded foundation for regulatory explainability.
SHARC Framework: It introduces a structured decomposition of SVaR into baseline, mean-driven, and volatility-driven components, enabling transparent interpretation of capital drivers within the Hybrid GPR-HS architecture.
Empirical Validation: It demonstrates that SHARC consistently aligns SVaR outputs with scenario designs across diverse macro scenarios, confirming framework fidelity and enabling auditable traceability.
Practical Governance Template: It translates SHARC decomposition into actionable risk governance rules, specifically:
- Capital Limit-Setting: When the mean component contributes >80% of SVaR (as observed in stress), risk managers should prioritize position reduction over volatility-based hedging (e.g., options), as variance-reducing hedges may be ineffective against directional loss magnitude.
- Scenario Validation: Inconsistencies between SHAP rankings and input shock magnitudes can flag scenario design errors.
- Reporting: Force plots serve as direct exhibits for ICAAP/CCAR submissions.

5. Conclusion

The paper concludes that SHARC transforms the Hybrid GPR-HS framework into a fully auditable capital engine. By resolving the "black box" problem, it allows institutions to leverage the predictive superiority of non-parametric ML models while meeting the strict transparency and documentation standards of FRTB, ICAAP, and CCAR. The findings suggest that under stress, capital requirements are driven more by directional loss magnitude than volatility expansion, a insight with direct implications for position management and hedging strategies. The framework is presented not merely as an academic exercise but as a production-ready tool for regulatory risk governance.