Module aad 

Adjoint Algorithmic Differentiation (AAD): tape-based reverse-mode differentiation for pricing code.

Write a pricer over Var instead of f64 — the operator overloading records every operation on a Tape — and one backward sweep (Var::grad) returns the sensitivity of the output to every input at once, at a fixed small multiple of the pricing cost. That is the AAD trade against bump-and-reprice: bumping costs one full reprice per input, the adjoint sweep costs ~one reprice total, however many inputs there are — the difference between seconds and hours on a book with per-pillar curve and surface sensitivities.

Two worked and tested quant applications live in this module’s tests:

• black_scholes: the closed form written over Var; a single sweep produces delta, dual delta, rho, carry rho, vega and the maturity sensitivity simultaneously, matching the library’s closed-form Greeks to near machine precision;
• pathwise Monte Carlo Greeks: differentiate through the simulation itself (one small tape per path), giving delta, vega and rho from the same paths that price — the standard pathwise estimator, validated against the closed forms.

The max(x, 0) payoff kink is handled by the almost-everywhere derivative (Var::maxf), which is exactly the classical pathwise estimator’s requirement (fine for vanillas and smooth-density payoffs; digitals need smoothing or likelihood-ratio methods).

Re-exports

pub use tape::Gradients;

pub use tape::Tape;

pub use var::Var;

Modules

tape

The AAD tape (Wengert list) and the backward sweep.

var

The differentiable value type: Var records every operation on the tape via operator overloading, so pricing code written over Var looks like ordinary arithmetic.

Functions

black_scholes

Black-Scholes price recorded on the tape: differentiate to get every first-order Greek from one backward sweep.