/**
 * @file black-scholes.ts
 * @description Black-Scholes option pricing formula and supporting statistical functions.
 * @author astra <astra@volare.finance>
 * @date 2022
 */
/**
 * Standard normal density function.
 * @description See {@link http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function|Wikipedia page}.
 * @param {Number} x The value to calculate the standard normal density of
 * @returns {Number} The value of the standard normal density function at x
 */
export declare function stdNormDensity(x: number): number;
/**
 * Standard normal cumulative distribution function.  The probability is estimated
 * by expanding the CDF into a series using the first 100 terms.
 * See {@link http://en.wikipedia.org/wiki/Normal_distribution#Cumulative_distribution_function|Wikipedia page}.
 *
 * @param {Number} x The upper bound to integrate over.  This is P{Z <= x} where Z is a standard normal random variable.
 * @returns {Number} The probability that a standard normal random variable will be less than or equal to x
 */
export declare function stdNormCDF(x: number): number;
/**
 * Black-Scholes option pricing formula.
 * See {@link http://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#Black-Scholes_formula|Wikipedia page}
 * for pricing puts in addition to calls.
 *
 * @param   {Number} s       Current price of the underlying
 * @param   {Number} k       Strike price
 * @param   {Number} t       Time to expatriation in years
 * @param   {Number} v       Volatility as a decimal
 * @param   {Number} r       Annual risk-free interest rate as a decimal
 * @param   {Boolean} isPut The type of option to be priced
 * @returns {Number}         Price of the option
 */
export declare function blackScholes(s: number, k: number, t: number, v: number, r: number, isPut: boolean): number;
/**
 * Calculate omega as defined in the Black-Scholes formula.
 *
 * @param   {Number} s Current price of the underlying
 * @param   {Number} k Strike price
 * @param   {Number} t Time to expatriation in years
 * @param   {Number} v Volatility as a decimal
 * @param   {Number} r Annual risk-free interest rate as a decimal
 * @returns {Number} The value of omega
 */
export declare function getW(s: number, k: number, t: number, v: number, r: number): number;