diff --git a/DIRECTORY.md b/DIRECTORY.md
index 564a7813807..be2a903d0cb 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -105,6 +105,7 @@
 * [Word Break](https://github.com/TheAlgorithms/Rust/blob/master/src/dynamic_programming/word_break.rs)
 * Financial
 * [Present Value](https://github.com/TheAlgorithms/Rust/blob/master/src/financial/present_value.rs)
+ * [Black Scholes](https://github.com/TheAlgorithms/Rust/blob/master/src/financial/black_scholes.rs)
 * General
 * [Convex Hull](https://github.com/TheAlgorithms/Rust/blob/master/src/general/convex_hull.rs)
 * [Fisher Yates Shuffle](https://github.com/TheAlgorithms/Rust/blob/master/src/general/fisher_yates_shuffle.rs)
diff --git a/src/financial/black_scholes.rs b/src/financial/black_scholes.rs
new file mode 100644
index 00000000000..a9bc7f348d6
--- /dev/null
+++ b/src/financial/black_scholes.rs
@@ -0,0 +1,92 @@
+/// implementation of the Black-Scholes model for option pricing
+/// The model essentially calculates the probability-weighted present value of the option's potential payoffs.
+/// The N(d1) and N(d2) terms represent probabilities related to the option finishing in-the-money (intrinsic value of the option).
+use std::f64::consts::PI;
+
+#[derive(PartialEq, Eq, Debug)]
+pub enum BlackScholesError {
+ InvalidParameters,
+}
+
+// accumulate standard normal distribution function
+fn normal_cdf(x: f64) -> f64 {
+ 0.5 * (1.0 + (x / (2.0_f64.sqrt() * PI)).exp().tanh())
+}
+
+// Round to 4 decimal
+fn round_to_precision(value: f64, precision: u32) -> f64 {
+ let multiplier = 10.0f64.powi(precision as i32);
+ (value * multiplier).round() / multiplier
+}
+
+pub fn black_scholes(
+ spot_price: f64, // current price of the stock
+ strike_price: f64, // price you can buy the stock at
+ time_to_maturity: f64, // time until the option expires (in years)
+ risk_free_rate: f64, // risk free interest rate (annualized)
+ volatility: f64,
+) -> Result<f64, BlackScholesError> {
+ if spot_price <= 0.0 + &#124;&#124; strike_price <= 0.0 + &#124;&#124; time_to_maturity < 0.0 + &#124;&#124; risk_free_rate < 0.0 + &#124;&#124; volatility < 0.0 + { + return Err(BlackScholesError::InvalidParameters); + } + + let d1 = (spot_price.ln() - strike_price.ln() + + (risk_free_rate + 0.5 * volatility.powi(2)) * time_to_maturity) + / (volatility * time_to_maturity.sqrt()); + let d2 = d1 - volatility * time_to_maturity.sqrt(); + + let n_d1 = normal_cdf(d1); + let n_d2 = normal_cdf(d2); + + let call_option_price = + spot_price * n_d1 - strike_price * (-risk_free_rate * time_to_maturity).exp() * n_d2; + + Ok(round_to_precision(call_option_price, 4)) +} + +#[cfg(test)] +mod tests { + use super::*; + macro_rules! test_black_scholes { + ($($name:ident: $inputs:expr,)*) => {
+ $(
+ #[test]
+ fn $name() {
+ let (spot_price, strike_price, time_to_maturity, risk_free_rate, volatility) = $inputs;
+ let expected = black_scholes(spot_price, strike_price, time_to_maturity, risk_free_rate, volatility).unwrap();
+ assert!(expected>= 0.0);
+ }
+ )*
+ }
+ }
+
+ macro_rules! test_black_scholes_Err {
+ ($($name:ident: $inputs:expr,)*) => {
+ $(
+ #[test]
+ fn $name() {
+ let (spot_price, strike_price, time_to_maturity, risk_free_rate, volatility) = $inputs;
+ assert_eq!(black_scholes(spot_price, strike_price, time_to_maturity, risk_free_rate, volatility).unwrap_err(), BlackScholesError::InvalidParameters);
+ }
+ )*
+ }
+ }
+
+ test_black_scholes! {
+ valid_parameters: (100.0, 100.0, 1.0, 0.05, 0.2),
+ another_valid_case: (150.0, 100.0, 2.0, 0.03, 0.25),
+ }
+
+ test_black_scholes_Err! {
+ negative_spot_price: (-100.0, 100.0, 1.0, 0.05, 0.2),
+ zero_strike_price: (100.0, 0.0, 1.0, 0.05, 0.2),
+ negative_time_to_maturity: (100.0, 100.0, -1.0, 0.05, 0.2),
+ negative_risk_free_rate: (100.0, 100.0, 1.0, -0.05, 0.2),
+ negative_volatility: (100.0, 100.0, 1.0, 0.05, -0.2),
+ }
+}
diff --git a/src/financial/mod.rs b/src/financial/mod.rs
index 89b36bfa5e0..f80a7d1e8b9 100644
--- a/src/financial/mod.rs
+++ b/src/financial/mod.rs
@@ -1,2 +1,5 @@
+mod black_scholes;
 mod present_value;
+
+pub use self::black_scholes::black_scholes;
 pub use present_value::present_value;
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