@insiderfinance/totalfinance/volatility/volatility-spot-beta

interface

VolatilitySpotBeta

The empirical vol–spot β and its regression diagnostics.

/** The empirical vol–spot β and its regression diagnostics. */
export interface VolatilitySpotBeta {
    /**
     * `β = ∂σ/∂S` in decimal vol **per $1 of spot** — feed straight to
     * `minimumVarianceDelta({ volatilitySpotBeta })`, which expects the same per-dollar units.
     *
     * Units matter here: `stickyRegime` reports `volatilitySpotBetaPerLogSpot` = `∂σ/∂lnS` (per 100%
     * spot move), which is `S ×` this number. On a `'log'` basis the conversion is done for you
     * (`slope / referenceSpot`); {@link slope} is the raw regression coefficient in its own basis.
     */
    volatilitySpotBeta: number;
    /** The regression slope: `∂σ/∂ln S` (`'log'`) or `∂σ/∂S` (`'level'`). */
    slope: number;
    /** Standard error of the slope. */
    slopeStandardError: number;
    /** t-statistic of the slope. */
    slopeTStatistic: number;
    /** Correlation of the IV change with the spot-change regressor (leverage ⇒ negative). */
    correlation: number;
    /** Coefficient of determination `R²`. */
    rSquared: number;
    /** Change observations used (after dropping bad pairs). */
    observationCount: number;
    /** Dropped (non-finite / non-positive) change observations. */
    dropped: number;
    /** Reference spot used for the `∂σ/∂S` conversion. */
    referenceSpot: number;
}

Fields, parameters & returned members (9)

Name / type	Meaning & unit	Optional / default
`correlation` `number`	Correlation of the IV change with the spot-change regressor (leverage ⇒ negative). unitless by name	Required / declared member No @default declared; consult the signature and description.
`dropped` `number`	Dropped (non-finite / non-positive) change observations. unitless by name	Required / declared member No @default declared; consult the signature and description.
`observationCount` `number`	Change observations used (after dropping bad pairs). count (integer)	Required / declared member No @default declared; consult the signature and description.
`rSquared` `number`	Coefficient of determination `R²`. unitless by name	Required / declared member No @default declared; consult the signature and description.
`referenceSpot` `number`	Reference spot used for the `∂σ/∂S` conversion. unitless by name	Required / declared member No @default declared; consult the signature and description.
`slope` `number`	The regression slope: `∂σ/∂ln S` (`'log'`) or `∂σ/∂S` (`'level'`). unitless by name	Required / declared member No @default declared; consult the signature and description.
`slopeStandardError` `number`	Standard error of the slope. unitless by name	Required / declared member No @default declared; consult the signature and description.
`slopeTStatistic` `number`	t-statistic of the slope. unitless by name	Required / declared member No @default declared; consult the signature and description.
`volatilitySpotBeta` `number`	`β = ∂σ/∂S` in decimal vol per $1 of spot — feed straight to `minimumVarianceDelta({ volatilitySpotBeta })`, which expects the same per-dollar units. Units matter here: `stickyRegime` reports `volatilitySpotBetaPerLogSpot` = `∂σ/∂lnS` (per 100% spot move), which is `S ×` this number. On a `'log'` basis the conversion is done for you (`slope / referenceSpot`); {@link slope} is the raw regression coefficient in its own basis. 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

VolatilitySpotBetaInput

Input for {@link estimateVolatilitySpotBeta}.

/** Input for {@link estimateVolatilitySpotBeta}. */
export interface VolatilitySpotBetaInput {
    /** Chronological spot prices. */
    spot: number[];
    /** The option's implied vol (decimal), aligned to `spot`. */
    impliedVolatility: number[];
    /** Regress IV changes on log-returns (`'log'`, default) or dollar spot changes (`'level'`). */
    basis?: 'log' | 'level';
    /** Reference spot to convert a log-basis slope to `∂σ/∂S` (default: the latest spot). */
    referenceSpot?: number;
    /** Newey–West HAC bandwidth for autocorrelation-robust errors. Default 0 uses classical standard errors (no HAC request). */
    hacLags?: number;
}

Fields, parameters & returned members (5)

Name / type	Meaning & unit	Optional / default
`basis` `'log' \| 'level'`	Regress IV changes on log-returns (`'log'`, default) or dollar spot changes (`'level'`). unitless by name	Optional No @default declared; consult the signature and description.
`hacLags` `number`	Newey–West HAC bandwidth for autocorrelation-robust errors. Default 0 uses classical standard errors (no HAC request). unitless by name	Optional No @default declared; consult the signature and description.
`impliedVolatility` `number[]`	The option's implied vol (decimal), aligned to `spot`. unitless by name	Required / declared member No @default declared; consult the signature and description.
`referenceSpot` `number`	Reference spot to convert a log-basis slope to `∂σ/∂S` (default: the latest spot). unitless by name	Optional No @default declared; consult the signature and description.
`spot` `number[]`	Chronological spot prices. 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

estimateVolatilitySpotBeta

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

export declare function estimateVolatilitySpotBeta(input: VolatilitySpotBetaInput): Computed<VolatilitySpotBeta, { measure: 'real-world-hedge'; basis: 'log' | 'level'; hacLags: number; }>;

Fields, parameters & returned members (10)

Name / type	Meaning & unit	Optional / default
`(input)` `VolatilitySpotBetaInput`	unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).basis` `'log' \| 'level'`	Regress IV changes on log-returns (`'log'`, default) or dollar spot changes (`'level'`). unitless by name	Optional No @default declared; consult the signature and description.
`(input).hacLags` `number`	Newey–West HAC bandwidth for autocorrelation-robust errors. Default 0 uses classical standard errors (no HAC request). unitless by name	Optional No @default declared; consult the signature and description.
`(input).impliedVolatility` `number[]`	The option's implied vol (decimal), aligned to `spot`. unitless by name	Required / declared member No @default declared; consult the signature and description.
`(input).referenceSpot` `number`	Reference spot to convert a log-basis slope to `∂σ/∂S` (default: the latest spot). unitless by name	Optional No @default declared; consult the signature and description.
`(input).spot` `number[]`	Chronological spot prices. unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.assumptions` `Assumptions<{ measure: 'real-world-hedge'; basis: 'log' \| 'level'; hacLags: number; }>`	Every applied convention, echoed back. unitless by name	Required / declared member No @default declared; consult the signature and description.
`return.diagnostics` `import('@insiderfinance/totalfinance/core').Diagnostics`	How the value was computed, plus any warnings. unitless by name	Required / declared member No @default declared; consult the signature and description.
`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.
`return.value` `VolatilitySpotBeta`	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.

Stability, warnings & conventions

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