Crate jaeckel 

Jaeckel

A Rust port of Peter Jäckel’s algorithms on http://www.jaeckel.org

Let’s Be Rational

The Rust crate is based on the latest (2024) version of the C++ reference implementation The conditionally compiled features in the C++ reference implementation are not included in this crate The PJ-2024-Inverse-Normal algorithm are used to inverse the normal cumulative distribution funciton and the AS241 algorighm is omitted

Example

use jaeckel::{black, implied_black_volatility};

// Calculate option price
let forward = 100.0;
let strike = 110.0;
let volatility = 0.2;
let time_to_expiry = 1.0;
let is_call = 1.0; // 1.0 for call, -1.0 for put

let price = black(forward, strike, volatility, time_to_expiry, is_call);

// Calculate implied volatility from price
let implied_vol = implied_black_volatility(price, forward, strike, time_to_expiry, is_call);
assert!((implied_vol - volatility).abs() < 1e-14);

Copyright

Original C++ implementation Copyright © 2013-2023 Peter Jäckel.

Permission to use, copy, modify, and distribute this software is freely granted, provided that this notice is preserved.

Functions

black

Calculate Black-Scholes option price.

convex_rational_cubic_control_parameter_to_fit_second_derivative_at_left_side

Calculate convex rational cubic control parameter to fit second derivative at left side.

convex_rational_cubic_control_parameter_to_fit_second_derivative_at_right_side

Calculate convex rational cubic control parameter to fit second derivative at right side.

erf_cody

Error function using Cody’s algorithm.

erfc_cody

Complementary error function using Cody’s algorithm.

erfcx_cody

Scaled complementary error function using Cody’s algorithm.

erfinv

Inverse error function.

householder3_factor

Householder’s third-order convergence factor for root finding.

householder4_factor

Householder’s fourth-order convergence factor for root finding.

implied_black_volatility

Calculate implied volatility from Black-Scholes price.

inverse_norm_cdf

Inverse cumulative normal distribution function.

minimum_rational_cubic_control_parameter

Calculate minimum rational cubic control parameter.

norm_cdf

Cumulative normal distribution function.

norm_pdf

Standard normal probability density function.

normalised_black

Calculate normalised Black-Scholes price.

normalised_implied_black_volatility

Calculate implied volatility from normalised Black-Scholes price.

normalised_vega

Calculate normalised vega.

normalised_volga

Calculate normalised volga.

rational_cubic_control_parameter_to_fit_second_derivative_at_left_side

Calculate control parameter to fit second derivative at left side.

rational_cubic_control_parameter_to_fit_second_derivative_at_right_side

Calculate control parameter to fit second derivative at right side.

rational_cubic_interpolation

Rational cubic interpolation function.

vega

Calculate Black-Scholes vega (price sensitivity to volatility).

volga

Calculate Black-Scholes volga (second derivative with respect to volatility).