Paper: arXiv 2305.06215

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.

Complexity vs Empirical Score

  • Math Complexity: 5.0/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]