@insiderfinance/totalfinance/options/black76

interface

Black76ImpliedVolatilityInput

Public declaration. Read the signature and parameter/member contracts below; no additional behavior is inferred.

export interface Black76ImpliedVolatilityInput {
    price: number;
    forward: number;
    strike: number;
    timeToExpiryYears: number;
    riskFreeRate: number;
    type: OptionType;
}

Fields, parameters & returned members (6)

Name / type	Meaning & unit	Optional / default
`forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

Declared field units are shown above. “Unitless by name” means the name alone does not establish a unit, not that a financial quantity has none. Check source descriptions, conventions, and the returned diagnostics. Errors and warnings are part of the result contract.

interface

Black76ImpliedVolatilityResult

Public declaration. Read the signature and parameter/member contracts below; no additional behavior is inferred.

export interface Black76ImpliedVolatilityResult {
    value: number;
    converged: boolean;
    iterations: number;
    reason?: 'below_intrinsic' | 'above_max_bound' | 'price_below_resolvable' | 'no_bracket' | 'max_iterations';
    /** Explanatory detail when a usable numeric pricing bracket cannot be established. */
    message?: string;
}

Fields, parameters & returned members (5)

Name / type	Meaning & unit	Optional / default
`converged` `boolean`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`iterations` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`message` `string`	Explanatory detail when a usable numeric pricing bracket cannot be established. unitless by name	Optional No @default declared; consult the signature and description.
`reason` `'below_intrinsic' \| 'above_max_bound' \| 'price_below_resolvable' \| 'no_bracket' \| 'max_iterations'`	unitless by name	Optional No @default declared; consult the signature and description.
`value` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

interface

Black76Input

Public declaration. Read the signature and parameter/member contracts below; no additional behavior is inferred.

export interface Black76Input {
    forward: number;
    strike: number;
    timeToExpiryYears: number;
    riskFreeRate: number;
    volatility: number;
}

Fields, parameters & returned members (5)

Name / type	Meaning & unit	Optional / default
`forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

type

Black76PriceBoundsInput

Public declaration. Read the signature and parameter/member contracts below; no additional behavior is inferred.

export type Black76PriceBoundsInput = Omit<Black76TypedInput, 'volatility'>;

Fields, parameters & returned members (5)

Name / type	Meaning & unit	Optional / default
`forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

interface

Black76TypedInput

Public declaration. Read the signature and parameter/member contracts below; no additional behavior is inferred.

export interface Black76TypedInput extends Black76Input {
    type: OptionType;
}

Fields, parameters & returned members (6)

Name / type	Meaning & unit	Optional / default
`forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

value

black76

The Black-76 facade namespace.

export declare const black76: { call: Facade<Black76Input, number>; extendedGreeks: Facade<Black76TypedInput, ExtendedGreeks>; greeks: Facade<Black76TypedInput, Greeks>; impliedVolatility: Facade<Black76ImpliedVolatilityInput, number, Record<never, never>, number | null>; price: Facade<Black76TypedInput, number>; put: Facade<Black76Input, number>; };

Fields, parameters & returned members (137)

Name / type	Meaning & unit	Optional / default
`call` `Facade<Black76Input, number>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call(input)` `Black76Input`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`call(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`call(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain` `(input: Black76Input) => Computed<number, Record<never, never>>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain().return.assumptions` `Assumptions<Record<never, never>>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain().return.diagnostics` `Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain().return.provenance` `import('@insiderfinance/totalfinance/core').Provenance`	Optional data lineage when the inputs came from a provider. unitless by name	Optional No @default declared; consult the signature and description.
`call.explain().return.value` `number`	The computed value. Never `NaN` or `±Infinity`: a value the model cannot produce is `null` beside a diagnostic that says why (Law 7 — a warning never licenses a non-finite number). unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain(input)` `Black76Input`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`call.explain(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`call.explain(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`call.explain(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks` `Facade<Black76TypedInput, ExtendedGreeks>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.charm` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.color` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.delta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.gamma` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.lambda` `number \| null`	Elasticity / effective leverage `Λ = Δ·S / V` (dimensionless). `null` when the price underflows to zero (deep-OTM): elasticity is undefined at V = 0 and is disclosed as null with a `greeks.lambda_undefined` warning on explained paths — never NaN/Infinity (Law 7). unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.phi` `number`	Dividend rho (epsilon) `ε = ∂V/∂q`, per 1% dividend yield (scaled like `rho`). unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.rho` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.speed` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.theta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.ultima` `number`	`∂vomma/∂σ = ∂³V/∂σ³` (raw). unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.vanna` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.vega` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.vera` `number`	`∂rho/∂σ = ∂²V/∂r∂σ` (raw, per 1.00 σ; rho here is per 1.00 rate). unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.veta` `number`	`∂vega/∂T` (raw, per year of time-to-expiry; vega here is per 1.00 σ) — the ∂/∂T sibling of vega. unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.vomma` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks().return.zomma` `number`	`∂Γ/∂σ = ∂³V/∂S²∂σ` (raw, per 1.00 σ). unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain` `(input: Black76TypedInput) => Computed<ExtendedGreeks, Record<never, never>>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain().return.assumptions` `Assumptions<Record<never, never>>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain().return.diagnostics` `Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain().return.provenance` `import('@insiderfinance/totalfinance/core').Provenance`	Optional data lineage when the inputs came from a provider. unitless by name	Optional No @default declared; consult the signature and description.
`extendedGreeks.explain().return.value` `ExtendedGreeks`	The computed value. Never `NaN` or `±Infinity`: a value the model cannot produce is `null` beside a diagnostic that says why (Law 7 — a warning never licenses a non-finite number). unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`extendedGreeks.explain(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks` `Facade<Black76TypedInput, Greeks>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks().return.delta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks().return.gamma` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks().return.rho` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks().return.theta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks().return.vega` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`greeks(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`greeks(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain` `(input: Black76TypedInput) => Computed<Greeks, Record<never, never>>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain().return.assumptions` `Assumptions<Record<never, never>>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain().return.diagnostics` `Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain().return.provenance` `import('@insiderfinance/totalfinance/core').Provenance`	Optional data lineage when the inputs came from a provider. unitless by name	Optional No @default declared; consult the signature and description.
`greeks.explain().return.value` `Greeks`	The computed value. Never `NaN` or `±Infinity`: a value the model cannot produce is `null` beside a diagnostic that says why (Law 7 — a warning never licenses a non-finite number). unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`greeks.explain(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility` `Facade<Black76ImpliedVolatilityInput, number, Record<never, never>, number \| null>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input)` `Black76ImpliedVolatilityInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input).price` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain` `(input: Black76ImpliedVolatilityInput) => Computed<number \| null, Record<never, never>>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain().return.assumptions` `Assumptions<Record<never, never>>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain().return.diagnostics` `Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain().return.provenance` `import('@insiderfinance/totalfinance/core').Provenance`	Optional data lineage when the inputs came from a provider. unitless by name	Optional No @default declared; consult the signature and description.
`impliedVolatility.explain().return.value` `number \| null`	The computed value. Never `NaN` or `±Infinity`: a value the model cannot produce is `null` beside a diagnostic that says why (Law 7 — a warning never licenses a non-finite number). unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input)` `Black76ImpliedVolatilityInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input).price` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`impliedVolatility.explain(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price` `Facade<Black76TypedInput, number>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`price(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`price(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain` `(input: Black76TypedInput) => Computed<number, Record<never, never>>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain().return.assumptions` `Assumptions<Record<never, never>>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain().return.diagnostics` `Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain().return.provenance` `import('@insiderfinance/totalfinance/core').Provenance`	Optional data lineage when the inputs came from a provider. unitless by name	Optional No @default declared; consult the signature and description.
`price.explain().return.value` `number`	The computed value. Never `NaN` or `±Infinity`: a value the model cannot produce is `null` beside a diagnostic that says why (Law 7 — a warning never licenses a non-finite number). unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`price.explain(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`price.explain(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`price.explain(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put` `Facade<Black76Input, number>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put(input)` `Black76Input`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`put(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`put(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain` `(input: Black76Input) => Computed<number, Record<never, never>>`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain().return.assumptions` `Assumptions<Record<never, never>>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain().return.diagnostics` `Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain().return.provenance` `import('@insiderfinance/totalfinance/core').Provenance`	Optional data lineage when the inputs came from a provider. unitless by name	Optional No @default declared; consult the signature and description.
`put.explain().return.value` `number`	The computed value. Never `NaN` or `±Infinity`: a value the model cannot produce is `null` beside a diagnostic that says why (Law 7 — a warning never licenses a non-finite number). unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain(input)` `Black76Input`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`put.explain(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`put.explain(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`put.explain(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

function

black76ExtendedGreeks

Black-76 higher-order Greeks (w.r.t. the forward `F`). The forward-price derivatives (vanna, charm, vomma, speed, color, zomma, veta, ultima) coincide with BSM's at `S = F`, `q = r` — Black-76 has the same `d1`/`d2` and discount as that BSM instance — so they are borrowed from {@link blackScholesExtendedGreeks}; the forward-model-specific ones are computed directly: - `vera` = ∂rho/∂σ = ∂(−T·price)/∂σ = −T·vega, - `phi` = 0 (the forward model has no dividend yield; carry is embedded in `F`), - `lambda` = Δ·F/V. First-order fields (theta/rho) come from {@link black76Greeks}, which are the Black-76 conventions.

export declare function black76ExtendedGreeks(input: Black76TypedInput): ExtendedGreeks;

Fields, parameters & returned members (23)

Name / type	Meaning & unit	Optional / default
`(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.charm` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.color` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.delta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.gamma` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.lambda` `number \| null`	Elasticity / effective leverage `Λ = Δ·S / V` (dimensionless). `null` when the price underflows to zero (deep-OTM): elasticity is undefined at V = 0 and is disclosed as null with a `greeks.lambda_undefined` warning on explained paths — never NaN/Infinity (Law 7). unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.phi` `number`	Dividend rho (epsilon) `ε = ∂V/∂q`, per 1% dividend yield (scaled like `rho`). unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.rho` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.speed` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.theta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.ultima` `number`	`∂vomma/∂σ = ∂³V/∂σ³` (raw). unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.vanna` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.vega` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.vera` `number`	`∂rho/∂σ = ∂²V/∂r∂σ` (raw, per 1.00 σ; rho here is per 1.00 rate). unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.veta` `number`	`∂vega/∂T` (raw, per year of time-to-expiry; vega here is per 1.00 σ) — the ∂/∂T sibling of vega. unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.vomma` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.zomma` `number`	`∂Γ/∂σ = ∂³V/∂S²∂σ` (raw, per 1.00 σ). unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

function

black76Greeks

Black-76 first-order Greeks (theta/day, vega/1%, rho/1%; delta/gamma w.r.t. the forward).

export declare function black76Greeks(input: Black76TypedInput): Greeks;

Fields, parameters & returned members (12)

Name / type	Meaning & unit	Optional / default
`(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.delta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.gamma` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.rho` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.theta` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.vega` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

function

black76ImpliedVolatility

Solve Black-76 implied volatility. Reports failure honestly; never fabricates a value. Bounds and endpoint acceptance follow the same RELATIVE-tolerance rules as the BSM kernel (see {@link impliedVolatilityPriceTolerance}): a target below the σ→0 price floor fails as `price_below_resolvable`, and a target at the σ→∞ upper bound as `above_max_bound`.

export declare function black76ImpliedVolatility(input: Black76ImpliedVolatilityInput): Black76ImpliedVolatilityResult;

Fields, parameters & returned members (12)

Name / type	Meaning & unit	Optional / default
`(input)` `Black76ImpliedVolatilityInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).price` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.converged` `boolean`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.iterations` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.message` `string`	Explanatory detail when a usable numeric pricing bracket cannot be established. unitless by name	Optional No @default declared; consult the signature and description.
`return.reason` `'below_intrinsic' \| 'above_max_bound' \| 'price_below_resolvable' \| 'no_bracket' \| 'max_iterations'`	unitless by name	Optional No @default declared; consult the signature and description.
`return.value` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

function

black76Price

Black-76 price. The second seed defect named in the spec, and the same shape as the first: omitting `volatility` made `sigma` `undefined`, `d1` `NaN`, and the returned price `NaN` — a success-typed wrong number.

export declare function black76Price(input: Black76TypedInput): number;

Fields, parameters & returned members (7)

Name / type	Meaning & unit	Optional / default
`(input)` `Black76TypedInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).volatility` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)

function

black76PriceBounds

No-arbitrage price bounds for Black-76.

export declare function black76PriceBounds(input: Black76PriceBoundsInput): { lower: number; upper: number; };

Fields, parameters & returned members (8)

Name / type	Meaning & unit	Optional / default
`(input)` `Black76PriceBoundsInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).forward` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).riskFreeRate` `number`	decimal rate (0.05 = 5%)	Required / declared member No @default declared; consult the signature and description.
`(input).strike` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).timeToExpiryYears` `number`	years (decimal)	Required / declared member No @default declared; consult the signature and description.
`(input).type` `OptionType`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.lower` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.upper` `number`	unitless by name	Required / declared member No @default declared; consult the signature and description.

Stability, warnings & conventions

stable-by-law (pre-1.0; not a 1.0 stability guarantee)