Risk Greeks via Finite-Difference Bumping
The daily-pain workload: 200-cell book, 5 Greeks, 9 full revaluations. LRDE delivers the same Greeks 40× faster.
- 40×
- Speedup vs scipy BDF
- 0.72 s
- Full Greek refresh
- 24 nμ
- Delta agreement (LRDE vs BDF)
- 5
- Greeks: Δ / Γ / vega / θ / ρ
The scenario
Set the picture
A risk desk needs a full Greek refresh on a 200-cell book: delta, gamma, vega, theta, rho. The standard production technique is bumping — each Greek is the central difference of two full book revaluations. That’s 9 full book revaluations (1 base + 8 bumped scenarios).
Today: 29 seconds. The desk refreshes once per hour instead of every tick because the math is the bottleneck.
Cost today
BDF total wall time: 28.7 seconds for 9 revaluations (3,184 ms per revaluation).
Refresh frequency is limited by compute, not market velocity. Greeks go stale between refreshes.
What changes with LRDE
LRDE amortizes the LU factorization across all 9 bumped scenarios. Total wall time: 0.72 seconds (80 ms per revaluation). Same Greeks to extraordinary precision.
Cross-method agreement: delta to 2.4 × 10⁻⁸, gamma to 2.9 × 10⁻⁸, vega to 5.8 × 10⁻⁵, rho to 3.2 × 10⁻⁴, theta to 4.3 × 10⁻⁶.
The desk can now refresh on every meaningful market move, not once per hour.
Measurable outcome
What we claim — and how it survives review
Each line below maps to a captured number in the demo section. Every number is reproducible from the benchmark suite.
- 40× speedup: 0.72 s vs 28.7 s for the full Greek refresh.
- Delta agreement between LRDE and BDF: 2.4 × 10⁻⁸ (24 nano-units per cell).
- Gamma agreement: 2.9 × 10⁻⁸ — both methods agree on the same noisy gamma estimate.
- All 5 Greeks computed via industry-standard bump sizes (ΔS ±1%, Δσ ±1 vol pt, Δr ±25 bps, ΔT ±1 day).
- SHA-256 of every Greek matrix for reproducibility.
The demo
What was tested. How. What the script printed.
A 50-strike × 4-maturity book = 200 cells. Price + 5 Greeks via central-difference bumping with industry-standard bump sizes. Total: 9 full book revaluations.
Honest caveat: the median relative error for gamma vs the closed form is ~50% — but both LRDE and BDF share this exact same value. Central-difference bumping is intrinsically noisy for second-order Greeks. The two solvers agree to 29 nano-units; they just both agree on a noisy gamma estimate.
Captured benchmark output
The numbers the script actually printed.
| Method | Total wall | Per-revaluation |
|---|---|---|
| LRDE | 0.72 s | 80 ms |
| BDF | 28.7 s | 3,184 ms |
| Greek | Max abs diff |
|---|---|
| Price | 7.7 × 10⁻⁶ |
| Delta | 2.4 × 10⁻⁸ |
| Gamma | 2.9 × 10⁻⁸ |
| Vega | 5.8 × 10⁻⁵ |
| Rho | 3.2 × 10⁻⁴ |
| Theta | 4.3 × 10⁻⁶ |
Composes with
Where this POC sits in the benchmark suite
POC 02
Vol Surface Revaluation
Greeks bump the vol surface — the LU from POC 2 is reused.
POC 04
Multi-Scenario Overnight Risk Fan-Out
Greeks under scenarios are the inner loop of overnight risk.
POC 05
SolvNum Audit & Compression Overlay
SolvNum compresses Greek matrices 4× at k=12 for downstream consumers.
Evidence pointers
Where the claims live in the repo
These are the files a reviewer should run to re-derive every number on this page.
- poc/lrde_hedge_fund/greeks_book/bench.py
- docs/pitch/LRDE_HEDGE_FUND_BRIEF.md §4
Want to see these numbers on your book?
Run the benchmark on your actual vol surface and trade book.
Two weeks, $25K, fully credited. No production integration, no data leaving your premises. Every claim above traces back to a script you can run locally.