Update copyright info, add library notices, and enhance documentation

Updated the copyright owner's name in the LICENSE file and added the license notice for the externally sourced library. Introduced detailed explanations for the `black` and `implied_black_volatility` functions in src/lets_be_rational.rs. Lastly, improved the introductory content in the README.md file to give a better overview of the project and its purpose.

LICENSE

@@ -1,6 +1,6 @@
 MIT License
 
-Copyright (c) 2024 hnakashima
+Copyright (c) 2024 Hikaru Nakashima
 
 Permission is hereby granted, free of charge, to any person obtaining a copy
 of this software and associated documentation files (the "Software"), to deal
@@ -19,3 +19,19 @@ AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 SOFTWARE.
+
+The externally maintained library from which parts of the Software is derived is:
+
+    - LetsBeRational, licensed as follows:
+
+    =========================================================================================
+     Copyright © 2013 - 2023 Peter Jäckel.
+
+     Permission to use, copy, modify, and distribute this software is freely granted,
+     provided that this notice is preserved.
+
+     WARRANTY DISCLAIMER
+     The Software is provided "as is" without warranty of any kind, either express or implied,
+     including without limitation any implied warranties of condition, uninterrupted use,
+     merchantability, fitness for a particular purpose, or non-infringement.
+    ==========================================================================================

README.md

@@ -1,2 +1,10 @@
-# implied-vol
-A pure rust implementation of Peter Jäckel's implied volatility calculation
+# Implied Vol
+
+Welcome to `implied-vol`, a lightning-fast, pure Rust implementation of Peter Jäckel's renowned implied volatility
+calculations.
+
+Originally found at [Peter Jäckel's homepage](http://www.jaeckel.org/), this library is a robust Rust reimplementation
+of the pioneering work laid out in Jäckel's article, [Let's Be Rational](http://www.jaeckel.org/LetsBeRational.pdf).
+
+Our aim is to offer a tool that provides blazingly fast and precise calculations of implied Black volatility.
+With `implied-vol`, speed and accuracy in your quantitative finance projects need not be mutually exclusive.

src/lets_be_rational.rs

@@ -183,6 +183,19 @@ fn normalised_black(x: f64, s: f64, theta: f64) -> f64 {
     normalised_black_call(if theta < 0f64 { -x } else { x }, s)
 }
 
+/// Calculates the price of a European option using the Black-Scholes formula.
+///
+/// # Arguments
+///
+/// * `f` - The current value of the underlying asset.
+/// * `k` - The strike price of the option.
+/// * `sigma` - The volatility of the underlying asset.
+/// * `t` - The time to expiration of the option.
+/// * `q` - Positive if call else put.
+///
+/// # Returns
+///
+/// The price of the European option.
 pub fn black(f: f64, k: f64, sigma: f64, t: f64, q: f64) -> f64 {
     let intrinsic = if q < 0f64 { k - f } else { f - k }.max(0f64).abs();
     if q * (f - k) > 0f64 {
@@ -452,6 +465,19 @@ fn implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(
 //     return unchecked_normalised_implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(beta, x, q, n);
 // }
 
+/// Calculates the implied black volatility using a transformed rational guess with limited iterations.
+///
+/// # Arguments
+///
+/// * `price` - The current price of the option.
+/// * `f` - The current forward price of the underlying asset.
+/// * `k` - The strike price of the option.
+/// * `t` - The time to expiration in years.
+/// * `q` - Positive if call else put.
+///
+/// # Returns
+///
+/// The implied black volatility.
 pub fn implied_black_volatility(price: f64, f: f64, k: f64, t: f64, q: f64) -> f64 {
     implied_volatility_from_a_transformed_rational_guess_with_limited_iterations(price, f, k, t, q, 2)
 }