Module greeks 

The central sensitivity engine: one implementation of bump-and-reprice Greeks, one batch entry point, engine-native fast paths.

Every Greek request routes through here. Engines fall into four routes:

• Grid (finite difference): delta/gamma/theta are read off the solved grid; the higher orders difference whole grid solutions (vanna = d(grid delta)/dσ), which is smoother than price stencils.
• Tree (binomial): same idea on the lattice — value and delta/gamma/theta from one backward pass, higher orders from bumped tree solutions (binomial::pricing_result shares seven passes).
• Analytic (Black-Scholes engine): the payoff-aware BlackScholesPricer with closed forms where they exist (vanilla vanna/charm/zomma/volga, the Black-76 futures family).
• Bump: everything else (Monte Carlo, Barone-Adesi-Whaley, Bjerksund-Stensland, analytic Heston) shares the one set of central-difference stencils below over EquityOption::price_with — the engine’s repricing kernel, which guarantees common random numbers under Monte Carlo. What used to be four hand-written copies of every stencil now differs only in a [BumpPolicy]: a per-engine table of bump sizes (preserved exactly, so values are bit-identical to the former per-engine code).

The batch entry point pricing_result shares evaluations across Greeks through a reprice cache: one Monte Carlo price() costs 17 simulations instead of 28, one finite-difference price() costs 9 solves instead of ~16.

Within the bump route, engines expose native fast paths where their structure allows a better estimator than a stencil: Monte Carlo pathwise delta/vega on the terminal-GBM route ([montecarlo::pathwise_delta_vega] — one simulation, no finite-difference bias), the adjoint (AAD) sweep on the path-simulation routes with continuous payoffs ([montecarlo::aad_greeks] — delta, vega and rho from one backward pass per path over the core::aad tape), the Heston vanilla delta read off the price integration ([heston::native_vanilla_delta]), and the Barone-Adesi-Whaley boundary solve shared across the spot ladder ([baw::SpotKernel], bit-identical values).

Functions

charm

delta

gamma

gamma_p

Delta elasticity S * gamma / delta; NaN when delta is zero.

pricing_result

Value plus all reported Greeks, sharing work across them: grid/tree engines harvest delta/gamma/theta from the base solve, and bump engines reuse every shifted reprice that appears in more than one stencil through the [Repricer] cache.

rho

theta

vanna

vega

volga

zomma