Solver

LRDE — PDE Pricing Without Time-Stepping

5–40× faster. Same prices. No time-stepping.

Every options pricing library solves the Black-Scholes PDE by marching through hundreds of time steps. LRDE computes the answer as a single contour integral in the Laplace domain. Cost is independent of maturity and stiffness; one LU factorization is reused across every strike, maturity, and scenario. The pricing inner loop gets 5–40× faster while producing the same prices to sub-basis-point precision.

Contour integral bypassing the time-stepping march, collapsing directly to the final price.

Imagine yourself in these moments. Same product, different industries.

Hedge-fund pricing

The vol surface that takes three minutes.

Your vol surface has 6,000 cells — 200 strikes times 30 maturities. Every time the market moves, the surface has to be re-priced. Today the inner loop is a time-stepper: Crank-Nicolson, BDF, ADI. It marches through hundreds of small steps from τ=0 to τ=T for every single cell. The 6,000-cell surface takes three minutes. The trader waits.

Imagine a pricing engine that computes the answer at T directly — one contour integral, one LU factorization reused across every strike in the same vol bucket. The 6,000-cell surface takes two seconds. The trader doesn’t wait.

Risk desk

The Greek refresh that holds up the desk.

A 200-cell book needs a full Greek refresh: delta, gamma, vega, theta, rho. That means nine full book revaluations (one base, eight bumped). Today: 29 seconds. The risk desk refreshes once per hour instead of every tick because the math is the bottleneck.

LRDE amortizes the LU factorization across all nine bumped scenarios. The same nine revaluations take 0.72 seconds. Same Greeks to 24 nano-units of delta. The desk refreshes on every meaningful move.

Overnight risk

The batch that was supposed to finish by 6 AM.

A 25-trade portfolio under 200 stochastic market scenarios. The overnight xVA fan-out is the bottleneck of every multi-strategy fund’s risk run. Tonight the scipy BDF baseline projects to 78 seconds. It is supposed to finish before the opening bell. Tonight, it will.

LRDE re-prices the entire fan-out in 6.6 seconds with production bucketing, 9.1 seconds head-to-head with no approximation. Same trade PVs to 29 micro-units. The VaR, Expected Shortfall, and FRTB capital numbers land before anyone arrives.