An Ultra-Low Latency Algorithm for Base Correlation Calibration in CDS Index Tranches
FlashCorr is a high-performance, analytically-driven algorithm that calibrates base correlations for credit index tranches (e.g., CDX.NA.IG, iTraxx Europe) using the Gaussian copula in the Large Homogeneous Portfolio (LHP) approximation. By reformulating the expected tranche loss into a closed-form bivariate normal expression and exploiting analytical cancellations in the derivatives, FlashCorr achieves over 100× speedup compared to traditional numerical quadrature + finite-difference approaches while converging to machine precision in typically 2–3 iterations.
- Closed-form Expected Loss using Drezner’s bivariate normal CDF (via QuantLib).
- Exact analytical gradient ("free gradient") derived from Plackett’s identity and a proven vanishing boundary term.
- Variance-stabilizing transformation (
z = arctanh(√ρ)) for robust convergence. - Halley’s method with analytical gradient + finite-difference Hessian for cubic convergence.
- Average 2.2 iterations and ~5.5 μs per calibration on a single Intel i9 core.
- Fully deterministic, no Monte Carlo noise.
- Apahce-2.0 licensed, production-ready C++17 implementation.
| Metric | Traditional (Quadrature + FD) | FlashCorr |
|---|---|---|
| Gradient method | Finite difference (bump) | Analytical (Plackett) |
| Iteration scheme | Secant / Brent | Halley (cubic) |
| Avg. iterations | ~12.5 | ~2.2 |
| Time per solve | ~650 μs | ~5.5 μs |
| Speedup | 1× | >100× |
FlashCorr depends on QuantLib (>= 1.28 recommended) for accurate bivariate normal evaluations.
# Clone the repository
git clone https://github.com/jialuechen/flashcorr.git
cd flashcorr
# Build with CMake (out-of-source build recommended)
mkdir build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j$(nproc)