From 664fa06b78945c64fc64177b83960a56918676ac Mon Sep 17 00:00:00 2001
From: Andy Pack <andy@sarsoo.xyz>
Date: Sun, 16 Feb 2025 23:36:55 +0000
Subject: [PATCH] working on black scholes options modelling
---
finlib/src/lib.rs | 1 +
finlib/src/options/blackscholes/mod.rs | 245 +++++++++++++++++++++++++
finlib/src/options/mod.rs | 1 +
3 files changed, 247 insertions(+)
create mode 100644 finlib/src/options/blackscholes/mod.rs
create mode 100644 finlib/src/options/mod.rs
diff --git a/finlib/src/lib.rs b/finlib/src/lib.rs
index 7dc8d0d..5024e04 100644
--- a/finlib/src/lib.rs
+++ b/finlib/src/lib.rs
@@ -5,6 +5,7 @@ pub mod stats;
pub mod util;
pub mod risk;
pub mod ffi;
+pub mod options;
#[cfg(feature = "parallel")]
use rayon::prelude::*;
diff --git a/finlib/src/options/blackscholes/mod.rs b/finlib/src/options/blackscholes/mod.rs
new file mode 100644
index 0000000..ec2af63
--- /dev/null
+++ b/finlib/src/options/blackscholes/mod.rs
@@ -0,0 +1,245 @@
+use statrs::distribution::{ContinuousCDF, Normal};
+
+#[derive(Debug, Copy, Clone, Default, PartialEq, PartialOrd)]
+pub struct OptionVariables {
+ underlying_price: f64,
+ strike_price: f64,
+ volatility: f64,
+ risk_free_interest_rate: f64,
+ dividend: f64,
+ time_to_expiration: f64
+}
+
+impl OptionVariables {
+
+ pub fn from(underlying_price: f64,
+ strike_price: f64,
+ volatility: f64,
+ risk_free_interest_rate: f64,
+ dividend: f64,
+ time_to_expiration: f64) -> Self {
+ Self {
+ underlying_price,
+ strike_price,
+ volatility,
+ risk_free_interest_rate,
+ dividend,
+ time_to_expiration,
+ }
+ }
+
+ pub fn call(self) -> CallOption {
+ let n = Normal::new(0., 1.0).unwrap();
+ let (d1, d2) = self.d1_d2();
+
+ let first = self.underlying_price * (-self.dividend * self.time_to_expiration).exp() * n.cdf(d1);
+
+ let second = self.strike_price * (-self.risk_free_interest_rate * self.time_to_expiration).exp() * n.cdf(d2);
+
+ CallOption::from(first - second, self)
+ }
+
+
+ pub fn put(self) -> PutOption {
+ let n = Normal::new(0., 1.0).unwrap();
+ let (d1, d2) = self.d1_d2();
+
+ let first = self.strike_price * (-self.risk_free_interest_rate * self.time_to_expiration).exp() * n.cdf(-d2);
+
+ let second = self.underlying_price * (-self.dividend * self.time_to_expiration).exp() * n.cdf(-d1);
+
+ PutOption::from(first - second, self)
+ }
+
+ pub fn d1_d2(&self) -> (f64, f64) {
+ let d1 = self.d1();
+
+ (d1, self.d2(d1))
+ }
+
+ pub fn d1(&self) -> f64 {
+
+ let first = (self.underlying_price / self.strike_price).log(std::f64::consts::E);
+
+ let second = self.time_to_expiration * (self.risk_free_interest_rate - self.dividend + (f64::powi(self.volatility, 2) / 2.));
+
+ let denominator = self.volatility * f64::sqrt(self.time_to_expiration);
+
+ (first + second) / denominator
+ }
+
+ pub fn d2(&self, d1: f64, ) -> f64 {
+ d1 - (self.volatility * f64::sqrt(self.time_to_expiration))
+ }
+}
+
+pub trait Option {
+ fn delta(&self) -> f64;
+ fn gamma(&self) -> f64;
+ fn vega(&self) -> f64;
+ fn theta(&self) -> f64;
+ fn rho(&self) -> f64;
+}
+
+#[derive(Debug, Copy, Clone, Default, PartialEq, PartialOrd)]
+pub struct CallOption {
+ pub price: f64,
+ pub variables: OptionVariables
+}
+
+impl CallOption {
+ pub fn from(price: f64, variables: OptionVariables) -> Self {
+ Self { price, variables }
+ }
+}
+
+impl Option for CallOption {
+ fn delta(&self) -> f64 {
+ let n = Normal::new(0., 1.0).unwrap();
+
+ (-self.variables.dividend * self.variables.time_to_expiration).exp() * n.cdf(self.variables.d1())
+ }
+
+ fn gamma(&self) -> f64 {
+ gamma(&self.variables)
+ }
+
+ fn vega(&self) -> f64 {
+ vega(&self.variables)
+ }
+
+ fn theta(&self) -> f64 {
+ todo!()
+ }
+
+ fn rho(&self) -> f64 {
+ todo!()
+ }
+}
+
+#[derive(Debug, Copy, Clone, Default, PartialEq, PartialOrd)]
+pub struct PutOption {
+ pub price: f64,
+ pub variables: OptionVariables
+}
+
+impl PutOption {
+ pub fn from(price: f64, variables: OptionVariables) -> Self {
+ Self { price, variables }
+ }
+}
+
+impl Option for PutOption {
+ fn delta(&self) -> f64 {
+ let n = Normal::new(0., 1.0).unwrap();
+
+ (-self.variables.dividend * self.variables.time_to_expiration).exp() * (n.cdf(self.variables.d1()) - 1.)
+ }
+
+ fn gamma(&self) -> f64 {
+ gamma(&self.variables)
+ }
+
+ fn vega(&self) -> f64 {
+ vega(&self.variables)
+ }
+
+ fn theta(&self) -> f64 {
+ todo!()
+ }
+
+ fn rho(&self) -> f64 {
+ todo!()
+ }
+}
+
+pub fn gamma(v: &OptionVariables) -> f64 {
+ let n = Normal::new(0., 1.0).unwrap();
+
+ let numerator = (-v.dividend * v.time_to_expiration).exp();
+ let denominator = v.underlying_price * v.volatility * f64::sqrt(v.time_to_expiration);
+
+ (numerator / denominator) * n.cdf(v.d1())
+}
+
+pub fn vega(v: &OptionVariables) -> f64 {
+ let n = Normal::new(0., 1.0).unwrap();
+
+ let numerator = (-v.dividend * v.time_to_expiration).exp();
+
+ v.underlying_price * numerator * f64::sqrt(v.time_to_expiration) * n.cdf(v.d1()) / 100.
+}
+
+#[cfg(test)]
+mod tests {
+ use super::*;
+
+ #[test]
+ fn call_test() {
+ let v = OptionVariables::from(100., 100., 0.25, 0.05, 0.01, 30./365.25);
+
+ let diff = (v.call().price - 3.019).abs();
+
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn put_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let diff = (v.put().price - 2.691).abs();
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn call_delta_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let diff = (v.call().delta() - 0.532).abs();
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn put_delta_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let delta = v.put().delta();
+ let diff = (delta - -0.467).abs();
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn gamma_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let gamma = v.put().gamma();
+ let diff = (gamma - 0.055).abs();
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn vega_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let vega = v.put().vega();
+ let diff = (vega - 11.390).abs();
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn call_rho_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let diff = (v.call().rho() - 4.126).abs();
+ assert!(diff < 0.01);
+ }
+
+ #[test]
+ fn put_rho_test() {
+ let v = OptionVariables::from(100., 100.,0.25, 0.05, 0.01, 30./365.25);
+
+ let rho = v.put().rho();
+ let diff = (rho - -4.060).abs();
+ assert!(diff < 0.01);
+ }
+}
\ No newline at end of file
diff --git a/finlib/src/options/mod.rs b/finlib/src/options/mod.rs
new file mode 100644
index 0000000..56dedb3
--- /dev/null
+++ b/finlib/src/options/mod.rs
@@ -0,0 +1 @@
+pub mod blackscholes;
\ No newline at end of file