The FRTB-IMA computational challenge for Equity Autocallables

ArXiv ID: 2305.06215 “View on arXiv”

Authors: Unknown

Abstract

When the Orthogonal Chebyshev Sliding Technique was introduced it was applied to a portfolio of swaps and swaptions within the context of the FRTB-IMA capital calculation. The computational cost associated to the computation of the ES values - an essential component of the capital caluclation under FRTB-IMA - was reduced by more than $90%$ while passing PLA tests. This paper extends the use of the Orthogonal Chebyshev Sliding Technique to portfolios of equity autocallables defined over a range of spot underlyings. Results are very positive as computational reductions are of about $90%$ with passing PLA metrics. Since equity autocallables are a commonly traded exotic trade type, with significant FRTB-IMA computational costs, the extension presented in this paper constitutes an imporant step forward in tackling the computational challenges associated to an efficient FRTB-IMA implementation.

Keywords: FRTB-IMA (Fundamental Review of the Trading Book - Internal Models Approach), Expected Shortfall (ES), Equity Autocallables, Orthogonal Chebyshev Sliding Technique, Capital Calculation, Equities / Exotic Derivatives

Complexity vs Empirical Score

• Math Complexity: 5.0/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical techniques like PCA and Chebyshev polynomials to reduce computational costs, indicating moderate-to-high math complexity. It demonstrates high empirical rigor by presenting specific computational reduction percentages (~95%), passing PLA test results, and detailed portfolio backtesting scenarios relevant to FRTB-IMA implementation.

  flowchart TD
    A["Research Goal:<br>Extend OCST to Equity Autocallables<br>to reduce FRTB-IMA ES computation cost"] --> B["Methodology:<br>Apply Orthogonal Chebyshev Sliding Technique"]
    B --> C["Data/Inputs:<br>Portfolio of Equity Autocallables<br>across varying spot underlyings"]
    C --> D["Computational Process:<br>Calculate Expected Shortfall<br>via OCST approximation"]
    D --> E{"Pass PLA Testing?"}
    E -- Yes --> F["Key Findings/Outcomes:<br>~90% Reduction in Computational Cost"]
    E -- No --> G["Refine Methodology"]
    G --> B
    F --> H["Significant Step Forward<br>for efficient FRTB-IMA Implementation"]