Crate black_76 

Black-76 option pricing model: closed-form prices, Greeks, and implied volatility solver for futures and forward options.

The Black-76 model (Fischer Black, The Pricing of Commodity Contracts, Journal of Financial Economics, 1976) prices European options on forward and futures contracts. Use it for Eurodollar options, FX forward options, commodity-futures options, and crypto perpetual-futures options where the underlying is a forward, not a spot.

Quick start

use black_76::{call_price, solve_iv, SolverConfig};

// Price an ATM call: F=100, K=100, T=1 year, sigma=20%, r=0
let c = call_price(100.0, 100.0, 1.0, 0.20, 0.0);
assert!((c - 7.9656).abs() < 1e-3);

// Solve for implied volatility given a market price
let cfg = SolverConfig::default();
let result = solve_iv(7.9656, 100.0, 100.0, 1.0, 0.0, true, &cfg);
assert!(result.converged);
assert!((result.iv - 0.20).abs() < 1e-4);

Modules

• pricing: closed-form Black-76 call/put prices, vega, intrinsic value.
• iv_solver: Newton-Raphson with Brent’s-method fallback.
• greeks: analytical first-order Greeks (delta, gamma, vega, theta, rho).
• inputs: BlackInputs / IvQuery typo-resistant, named-field wrappers.
• types: OptionType, SolverMethod, SolverResult, SolverStatus, InstrumentGreeks.
• config: SolverConfig (with builder) for tuning solver parameters.
• vol_surface (feature vol-surface): per-expiry IV smile with linear interpolation.
• digital (feature digital): risk-neutral probability extraction via call-spread replication and N(d2).

Feature flags

• serde: adds Serialize / Deserialize derives on public types.
• vol-surface: enables vol_surface.
• digital: enables digital (requires vol-surface).

Convergence checking

iv_solver::solve_iv returns a SolverResult whose converged: bool field MUST be checked before consuming iv. Whenever the solver does not converge, iv is f64::NAN and SolverStatus reports the precise reason (non-finite input, near-expiry, below intrinsic, non-positive price, no root in [iv_min, iv_max], vega-floor non-identifiability, or max iterations).

Equality and NaN

The f64-bearing public types that derive PartialEq (e.g. BlackInputs, SolverConfig) inherit IEEE-754 semantics, so a value holding a NaN is never equal to itself. This matters here because NaN is a first-class sentinel: the solver yields iv = NaN on every non-converged path. (Accordingly, SolverResult deliberately does not derive PartialEq.)

Re-exports

pub use config::SolverConfig;

pub use greeks::compute_greeks;

pub use inputs::BlackInputs;

pub use inputs::IvQuery;

pub use iv_solver::solve_iv;

pub use iv_solver::solve_iv_triple;

pub use pricing::call_price;

pub use pricing::d1_d2;

pub use pricing::intrinsic_value;

pub use pricing::price;

pub use pricing::put_price;

pub use pricing::vega;

pub use types::InstrumentGreeks;

pub use types::OptionType;

pub use types::SolverMethod;

pub use types::SolverResult;

pub use types::SolverStatus;

Modules

config

Solver configuration.

digitaldigital

Risk-neutral probability extraction via call-spread replication and N(d2).

greeks

First-order Greeks for Black-76 options.

inputs

Ergonomic, typo-resistant input structs.

iv_solver

Implied volatility solver with Newton-Raphson + Brent fallback.

pricing

Black-76 closed-form pricing.

types

Core types: OptionType, SolverMethod, SolverStatus, SolverResult, InstrumentGreeks.

vol_surfacevol-surface

Per-expiry implied volatility smile with linear-in-strike interpolation.