Engine snapshot — real output, recorded, not live
The tables below are genuine output from the pricing engine, committed to this site
as a fixed snapshot. They are not market data and they do not update on a schedule:
the engine is deterministic under fixed seeds, so these figures change only when the
engine changes.
One book, five methods
The same underlying priced across the model and method surface. Monte Carlo rows carry
a standard error and a 95% confidence interval; closed-form and PDE rows are exact for
their method.
Greeks, cross-checked
Each Greek is computed by a hand-written reverse-mode AAD tape and independently by
central finite differences with common random numbers; on the machine that produced
this snapshot a third check by JAX was also available. Each row states the tolerance
it was held to. Where a check is unavailable the cell says so, and where the methods
disagree the row is flagged rather than hidden.
In the live API the JAX column is n/a: server-side verification
is AAD against finite differences. The claim is not that every Greek everywhere is checked
three ways — it is that whatever checks ran are shown, with their tolerances.
Monte Carlo convergence
Standard error against path count for the European put, with the closed-form value as
the reference line. The shaded band is ±1.96 standard errors — it should narrow as
1/√N.
Implied volatility round-trip
Price → σ → price. The solver recovers the input volatility, and repricing at the
recovered σ returns the original price.
Provenance — how these numbers were produced