BSM Greeks: theta, rho, phi, zeta, strike-delta, strike-gamma.

CHANGELOG.md

@@ -2,6 +2,10 @@
 
 ## 17 September 2023
 
+- @avhz: More Greeks for BSM model: theta, rho, phi, zeta, strike-delta, strike-gamma.
+
+## 17 September 2023
+
 - @avhz: More Greeks for BSM model: vega, vomma, ultima, vega bleed (adding more soon).
 
 ## 16 September 2023

Cargo.toml

@@ -16,7 +16,7 @@
 name = "RustQuant"
 authors = ["avhz <[email protected]>"]
 description = "A Rust library for quantitative finance tools."
-version = "0.0.30"
+version = "0.0.31"
 edition = "2021"
 readme = "README.md"
 repository = "https://github.com/avhz/RustQuant"

src/instruments/options/black_scholes_merton.rs

@@ -7,6 +7,15 @@
 //      - LICENSE-MIT.md
 // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+//! The generalised Black-Scholes-Merton European Option pricing model.
+//!
+//! The differing cost of carry factor allows for the following models:
+//!     1. b = r:           Black-Scholes 1973 stock option model.
+//!     2. b = r - q:       Merton 1973 stock option model with continuous dividend yield.
+//!     3. b = 0:           Black 1976 futures option model.
+//!     4. b = 0, r = 0:    Asay 1982 margined futures option model.
+//!     5. b = r_d - r_f:   Garman and Kohlhagen 1983 currency option model.
+
 // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 // IMPORTS
 // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -279,6 +288,96 @@ impl BlackScholesMerton {
 
         self.vega() * (r - b + b * d1 / (v * T.sqrt()) - (d1 * d2 + 1.0) / (2.0 * T))
     }
+
+    /// Theta of the generalised Black-Scholes European option.
+    /// Also known as Expected Bleed.
+    pub fn theta(&self) -> f64 {
+        let (S, K, v, r, b) = self.unpack();
+        let T = self.year_fraction();
+        let (d1, d2) = self.d1_d2();
+
+        let n = Gaussian::default();
+
+        match self.option_type {
+            TypeFlag::Call => {
+                -S * ((b - r) * T).exp() * n.pdf(d1) * v / (2.0 * T.sqrt())
+                    - (b - r) * S * ((b - r) * T).exp() * n.cdf(d1)
+                    - r * K * (-r * T).exp() * n.cdf(d2)
+            }
+            TypeFlag::Put => {
+                -S * ((b - r) * T).exp() * n.pdf(d1) * v / (2.0 * T.sqrt())
+                    + (b - r) * S * ((b - r) * T).exp() * n.cdf(-d1)
+                    + r * K * (-r * T).exp() * n.cdf(-d2)
+            }
+        }
+    }
+
+    /// Rho of the generalised Black-Scholes European option.
+    pub fn rho(&self) -> f64 {
+        let T = self.year_fraction();
+
+        match self.option_type {
+            TypeFlag::Call => {
+                self.strike_price
+                    * T
+                    * (-self.risk_free_rate * T).exp()
+                    * Gaussian::default().cdf(self.d1_d2().1)
+            }
+            TypeFlag::Put => {
+                -self.strike_price
+                    * T
+                    * (-self.risk_free_rate * T).exp()
+                    * Gaussian::default().cdf(-self.d1_d2().1)
+            }
+        }
+    }
+
+    /// Phi of the generalised Black-Scholes European option.
+    /// Also known as Rho-2.
+    pub fn phi(&self) -> f64 {
+        let (S, _, _, r, b) = self.unpack();
+        let T = self.year_fraction();
+
+        let (d1, _) = self.d1_d2();
+
+        match self.option_type {
+            TypeFlag::Call => -T * S * ((b - r) * T).exp() * Gaussian::default().cdf(d1),
+            TypeFlag::Put => T * S * ((b - r) * T).exp() * Gaussian::default().cdf(-d1),
+        }
+    }
+
+    /// Zeta of the generalised Black-Scholes European option.
+    /// Also known as the in-the-money probability.
+    pub fn zeta(&self) -> f64 {
+        let n = Gaussian::default();
+
+        match self.option_type {
+            TypeFlag::Call => n.cdf(self.d1_d2().1),
+            TypeFlag::Put => n.cdf(-self.d1_d2().1),
+        }
+    }
+
+    /// Strike Delta of the generalised Black-Scholes European option.
+    /// Also known as Dual Delta or Discounted Probability.
+    pub fn strike_delta(&self) -> f64 {
+        let n = Gaussian::default();
+
+        let T = self.year_fraction();
+
+        match self.option_type {
+            TypeFlag::Call => -(-self.risk_free_rate * T).exp() * n.cdf(self.d1_d2().1),
+            TypeFlag::Put => (-self.risk_free_rate * T).exp() * n.cdf(-self.d1_d2().1),
+        }
+    }
+
+    /// Strike Gamma of the generalised Black-Scholes European option.
+    pub fn strike_gamma(&self) -> f64 {
+        let n = Gaussian::default();
+        let T = self.year_fraction();
+
+        n.pdf(self.d1_d2().1) * (-self.risk_free_rate * T).exp()
+            / (self.strike_price * self.volatility * T.sqrt())
+    }
 }
 
 // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~