Quantitative finance calculators for pricing, risk, and calibration.

The mechanic that makes a single Monte-Carlo run yield the price and every first-order sensitivity.

What actually happens between writing plain Java and getting a priced, differentiated result.

ADouble: what it tracks, and why an ordinary double can't be differentiated after the fact.

A plain Java function, run once, becomes a replayable computational graph.

A European call, priced and differentiated in one adjoint sweep — delta, vega, rho and strike sensitivity, no separate bump run per Greek.

Reconciling one adjoint sweep against independent forward revaluations, factor by factor.

A cross-Greek or cash-flow-timing sensitivity you didn't explicitly ask for, recovered for free from the same tape.

Prescribed up- and down-shock revaluations, reduced to one capital number per risk factor.

Delta, vega and curvature combined across risk classes into a single SA capital number.

CVA sensitivities from one AAD sweep on a real netting set, cross-checked against the regulation's own prescribed bump-and-revalue method.

Industry-standard initial margin, built from the same sensitivities your desk already has.

A prescribed shock set, replayed against the existing tape.

Long-horizon scenario pathways translated into the same market-shock language as any other stress test.

Copula and recursive loss-distribution pricing, cross-checked on the same portfolio.

Where a discontinuous jump process breaks naive smoothing, and how adjoint AD still returns a clean sensitivity.

Assembling unilateral CVA from its three regulatory components, explicitly.

The hedgeable sensitivities behind a CVA number — not just the capital charge.

The non-modelled Basic Approach number, for comparison against SA-CVA.

Historical, parametric and Monte Carlo routes to the same risk number, reconciled.

Kupiec and Christoffersen exception tests, the way a model-validation team runs them.

A scenario language that composes shocks without re-recording the underlying book.

Netting and diversification, and where naive summation overstates risk.

L-BFGS against adjoint gradients: three SABR parameters recovered from market vols, one adjoint sweep per iteration instead of one per finite difference.

Stochastic-vol calibration where adjoint gradients replace a finite-difference Jacobian.

The COS method's own closed-form route, for when recording overhead isn't worth paying.

Each instrument's sensitivity to every curve point, recovered from one recorded bootstrap.

When calibration goes through a solver, not a sweep — and what that means for its Greeks.

Where the recording itself becomes the engineering constraint.

Path-averaged payoffs differentiate the same way vanilla ones do.

Discontinuous payoffs, and what smoothing costs you in exchange for a usable sensitivity.

Bring your own payoff function and get full sensitivities without touching the engine.

Correlated underlyings, one tape, every pairwise sensitivity.

Two correlated legs, one payoff, differentiated jointly.

Cross-currency drift correction and the other measure-mismatch adjustments — closed-form, the same way the Java source computes them, not on the AAD tape.

A binomial lattice, recorded and differentiated through every branch.

Longstaff-Schwartz regression exercise, and the honest limits of its sensitivity.

The same recording, replayed on six backends without touching the valuation code.

What gets dropped on replay for performance, and reconstructed only when needed.

Four GPU codegen paths generated from the identical tape.

What the Class-File API actually emits for a recorded valuation.

Writing a custom op: forward value and adjoint rule, both required.

WGSL or PTX, generated, not hand-written — line by line.