feat: update cgmy

Author: dancixx

src/stats.rs

@@ -1,3 +1,4 @@
 pub mod cir;
 pub mod fd;
 pub mod mle;
+pub mod non_central_chi_squared;

src/stats/non_central_chi_squared.rs

@@ -0,0 +1,13 @@
+use rand_distr::{ChiSquared, Distribution, Normal};
+
+pub fn sample(df: f64, non_centrality: f64) -> f64 {
+  let mut rng = rand::thread_rng();
+
+  let chi_squared = ChiSquared::new(df).unwrap();
+  let central_part: f64 = chi_squared.sample(&mut rng);
+
+  let normal_dist = Normal::new(non_centrality.sqrt(), 1.0).unwrap();
+  let non_central_part: f64 = normal_dist.sample(&mut rng).powi(2);
+
+  central_part + non_central_part
+}

src/stochastic/jump/cgmy.rs

@@ -1,8 +1,9 @@
 use crate::stochastic::{process::poisson::Poisson, Sampling};
 use impl_new_derive::ImplNew;
 use ndarray::Array1;
-use rand::{thread_rng, Rng};
-use rand_distr::Exp;
+use ndarray_rand::RandomExt;
+use rand::Rng;
+use rand_distr::{Exp, Uniform};
 use scilib::math::basic::gamma;
 
 /// CGMY process
@@ -69,27 +70,25 @@ impl Sampling<f64> for CGMY {
       * gamma(1.0 - self.alpha)
       * (self.lambda_plus.powf(self.alpha - 1.0) - self.lambda_minus.powf(self.alpha - 1.0));
 
-    let mut rng = thread_rng();
+    let U = Array1::<f64>::random(self.j, Uniform::new(0.0, 1.0));
+    let E = Array1::<f64>::random(self.j, Exp::new(1.0).unwrap());
+    let poisson = Poisson::new(1.0, Some(self.j), None, None);
+    let poisson = poisson.sample();
+
+    let mut rng = rand::thread_rng();
 
     for i in 1..self.n {
       let mut jump_component = 0.0;
 
-      let poisson = Poisson::new(1.0, Some(self.j), None, None);
-      let poisson = poisson.sample();
-
-      for j in 0..self.j {
-        let u_j: f64 = rng.gen();
-        let e_j: f64 = rng.sample(Exp::new(1.0).unwrap());
-
+      for j in 1..self.j {
         let v_j = if rng.gen_bool(0.5) {
           self.lambda_plus
         } else {
           -self.lambda_minus
         };
 
         let term1 = (self.alpha * poisson[j] / (2.0 * c)).powf(-1.0 / self.alpha);
-        let term2 = e_j * u_j.powf(1.0 / self.alpha) / v_j.abs();
-
+        let term2 = E[j] * U[j].powf(1.0 / self.alpha) / v_j.abs();
         let jump_size = term1.min(term2) * (v_j / v_j.abs());
 
         jump_component += jump_size;
@@ -119,50 +118,19 @@ mod tests {
 
   #[test]
   fn cgmy_length_equals_n() {
-    let cgmy = CGMY {
-      lambda_plus: 5.0,
-      lambda_minus: 5.0,
-      alpha: 0.7,
-      n: N,
-      j: 1000,
-      x0: Some(0.0),
-      t: Some(1.0),
-      m: None,
-    };
-
+    let cgmy = CGMY::new(5.0, 5.0, 0.7, N, 1000, Some(0.0), Some(1.0), None);
     assert_eq!(cgmy.sample().len(), N);
   }
 
   #[test]
   fn cgmy_starts_with_x0() {
-    let cgmy = CGMY {
-      lambda_plus: 5.0,
-      lambda_minus: 5.0,
-      alpha: 0.7,
-      n: N,
-      j: 1000,
-      x0: Some(0.0),
-      t: Some(1.0),
-      m: None,
-    };
-
+    let cgmy = CGMY::new(5.0, 5.0, 0.7, N, 1000, Some(0.0), Some(1.0), None);
     assert_eq!(cgmy.sample()[0], 0.0);
   }
 
   #[test]
   fn cgmy_plot() {
-    let cgmy = CGMY {
-      lambda_plus: 5.0,
-      lambda_minus: 5.0,
-      alpha: 0.7,
-      n: 1000,
-      j: 1000,
-      x0: Some(0.0),
-      t: Some(1.0),
-      m: None,
-    };
-
-    // Plot the CGMY sample path
+    let cgmy = CGMY::new(25.46, 4.604, 0.52, 100, 1024, Some(2.0), Some(1.0), None);
     plot_1d!(cgmy.sample(), "CGMY Process");
   }
 }

src/stochastic/volatility.rs

@@ -3,6 +3,7 @@ pub mod fheston;
 pub mod heston;
 pub mod rbergomi;
 pub mod sabr;
+pub mod svcgmy;
 
 #[derive(Debug, Clone, Copy, Default)]
 pub enum HestonPow {

src/stochastic/volatility/svcgmy.rs

@@ -0,0 +1,187 @@
+use impl_new_derive::ImplNew;
+use ndarray::{s, Array1};
+use ndarray_rand::RandomExt;
+use rand::Rng;
+use rand_distr::{Exp, Uniform};
+use scilib::math::basic::gamma;
+
+use crate::{
+  stats::non_central_chi_squared,
+  stochastic::{process::poisson::Poisson, Sampling},
+};
+
+#[derive(ImplNew)]
+pub struct SVCGMY {
+  /// Positive jump rate lambda_plus (corresponds to G)
+  pub lambda_plus: f64, // G
+  /// Negative jump rate lambda_minus (corresponds to M)
+  pub lambda_minus: f64, // M
+  /// Jump activity parameter alpha (corresponds to Y), with 0 < alpha < 2
+  pub alpha: f64,
+  ///
+  pub kappa: f64,
+  ///
+  pub eta: f64,
+  ///
+  pub zeta: f64,
+  ///
+  pub rho: f64,
+  /// Number of time steps
+  pub n: usize,
+  /// Jumps
+  pub j: usize,
+  ///
+  pub x0: Option<f64>,
+  /// Initial value
+  pub v0: Option<f64>,
+  /// Total time horizon
+  pub t: Option<f64>,
+  /// Number of samples for parallel sampling (not used in this implementation)
+  pub m: Option<usize>,
+}
+
+impl Sampling<f64> for SVCGMY {
+  fn sample(&self) -> Array1<f64> {
+    let t_max = self.t.unwrap_or(1.0);
+    let dt = self.t.unwrap_or(1.0) / (self.n - 1) as f64;
+    let mut x = Array1::<f64>::zeros(self.n);
+    x[0] = self.x0.unwrap_or(0.0);
+
+    let C = (gamma(2.0 - self.alpha)
+      * (self.lambda_plus.powf(self.alpha - 2.0) + self.lambda_minus.powf(self.alpha - 2.0)))
+    .powi(-1);
+    let c = (2.0 * self.kappa) / ((1.0 - (-self.kappa * dt).exp()) * self.zeta.powi(2));
+
+    let mut v = Array1::<f64>::zeros(self.n);
+    v[0] = self.v0.unwrap_or(0.0);
+
+    for i in 1..self.n {
+      let xi = non_central_chi_squared::sample(
+        4.0 * self.kappa * self.eta / self.zeta.powi(2),
+        2.0 * c * v[i - 1] * (-self.kappa * dt).exp(),
+      );
+
+      v[i] = xi / (2.0 * c);
+    }
+
+    let U = Array1::<f64>::random(self.j, Uniform::new(0.0, 1.0));
+    let E = Array1::<f64>::random(self.j, Exp::new(1.0).unwrap());
+    let E_ = Array1::<f64>::random(self.j, Exp::new(1.0).unwrap());
+    let P = Poisson::new(1.0, Some(self.j), None, None);
+    let mut P = P.sample();
+
+    for (idx, p) in P.iter_mut().enumerate() {
+      *p = *p + E_[idx];
+    }
+
+    let tau = Array1::<f64>::random(self.j, Uniform::new(0.0, t_max));
+    let mut c_t = Array1::<f64>::zeros(self.j);
+
+    for j in 1..self.j {
+      c_t[j] = C * v.slice(s![..j - 1]).sum()
+    }
+
+    let mut rng = rand::thread_rng();
+
+    for i in 1..self.n {
+      let mut jump_component = 0.0;
+
+      for j in 1..self.j {
+        let v_j = if rng.gen_bool(0.5) {
+          self.lambda_plus
+        } else {
+          -self.lambda_minus
+        };
+
+        let term1 = ((self.alpha * P[j]) / (2.0 * c_t[j] * t_max)).powf(-1.0 / self.alpha);
+        let term2 = E[j] * U[j].powf(1.0 / self.alpha) / v_j.abs();
+        let jump_size = term1.min(term2) * (v_j / v_j.abs());
+
+        jump_component += jump_size;
+      }
+
+      let b = -(v[i]
+        * (self.lambda_plus.powf(self.alpha - 1.0) - self.lambda_minus.powf(self.alpha - 1.0))
+        / ((1.0 - self.alpha)
+          * (self.lambda_plus.powf(self.alpha - 2.0) + self.lambda_minus.powf(self.alpha) - 2.0)));
+
+      x[i] = x[i - 1] + jump_component + b * dt + self.rho * v[i - 1];
+    }
+
+    x
+  }
+
+  fn n(&self) -> usize {
+    self.n
+  }
+
+  fn m(&self) -> Option<usize> {
+    self.m
+  }
+}
+
+#[cfg(test)]
+mod tests {
+  use super::*;
+  use crate::{plot_1d, stochastic::N};
+
+  #[test]
+  fn svcgmy_length_equals_n() {
+    let svcgmy = SVCGMY::new(
+      25.46,
+      4.604,
+      0.52,
+      1.003,
+      0.0711,
+      0.3443,
+      -2.0280,
+      N,
+      1024,
+      None,
+      Some(0.0064),
+      Some(1.0),
+      None,
+    );
+    assert_eq!(svcgmy.sample().len(), N);
+  }
+
+  #[test]
+  fn svcgmy_starts_with_x0() {
+    let svcgmy = SVCGMY::new(
+      25.46,
+      4.604,
+      0.52,
+      1.003,
+      0.0711,
+      0.3443,
+      -2.0280,
+      N,
+      1024,
+      None,
+      Some(0.0064),
+      Some(1.0),
+      None,
+    );
+    assert_eq!(svcgmy.sample()[0], 0.0);
+  }
+
+  #[test]
+  fn svcgmy_plot() {
+    let svcgmy = SVCGMY::new(
+      25.46,
+      4.604,
+      0.52,
+      1.003,
+      0.0711,
+      0.3443,
+      -2.0280,
+      100,
+      1024,
+      None,
+      Some(0.0064),
+      Some(1.0),
+      None,
+    );
+    plot_1d!(svcgmy.sample(), "CGMY Process");
+  }
+}