The Problem

The Internal Model Approach (IMA) in FRTB presents significant challenges, a central one being the P&L Attribution Test (PLA Test). Institutions must pass stringent statistical tests to validate the pricing models used in the Expected Shortfall (ES) calculation. A brute-force solution is to use the official Front Office (FO) pricing models directly in the ES calculation. This solution would comply with the regulatory PLA Test, but it results in severe compute costs, especially for books of exotic derivatives.

The Solution

MoCaX’s Smart Sampling Machine Learning techniques enable efficient calibration of pricing models using very few sampling points. This approach replicates the behavior of exotic pricing models with high accuracy, ensuring that the PLA Test remains well within regulatory compliance.

Once the Machine Learning model is calibrated using the proprietary Smart Sampling techniques, it can be executed ultra-efficiently, reducing computational costs significantly. The result is an FRTB IMA framework that operates at typically less than 10% of the traditional compute cost.

Numerical Results

We demonstrate the efficiency of MoCaX’s technology through two key use cases:

1. Equity Autocallables

A capital calculation under FRTB IMA was performed on a portfolio of 450 Equity Autocallables, each with up to 10 underlying assets. The IMA calculations required revaluations in 1,500 scenarios, incorporating different Liquidity Horizons and periods of stress.

MoCaX’s Smart Sampling techniques reduced the pricing effort to just 80 “Smart” scenarios, from which the proprietary Machine Learning (ML)-based models, grounded on the exponential convergence of Chebyshev Tensors, was calibrated. This ML model was then evaluated across all 1,500 scenarios in an ultra-efficient manner.

The resulting outputs shown below demonstrate a strong correlation between the FO pricing model and MoCaX’s calibrated Machine Learning model.

Furthermore, the accuracy was validated through the PLA Test, where both the Correlation and Kolmogorov-Smirnov test results fell well within the Green regulatory zone, demonstrating MoCaX’s exceptional accuracy.

Computational Efficiency:

• The entire computation, including ML model calibration, required only 5.3% of the compute effort compared to a brute-force approach that calls FO pricing models in each scenario.
• This led to a substantial reduction in cloud computing costs and improved time efficiency.

2. FX TARFs (Target Accrual Redemption Forwards)

A similar test was conducted on a portfolio of FX TARFs, where MoCaX’s proprietary Machine Learning methods required only 71 “Smart” scenarios for calibration while maintaining very high accuracy well inside the green zone of the PLA Test, as shown in the following exhibit.

Conclusion

MoCaX Intelligence delivers cutting-edge AI-driven computational solutions, making FRTB IMA compliance more efficient while dramatically reducing compute costs and accelerating calculations.

For further details on MoCaX techniques for FRTB IMA, you can read this paper.