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use num_complex::Complex;
pub fn gamma_cf(u: &Complex<f64>, a: f64, b: f64) -> Complex<f64> {
(1.0 - u * b).powf(-a)
}
pub fn gamma_leverage(
t: f64,
v0: f64,
a: f64,
sigma: f64,
lambda: f64,
correlation: f64,
alpha: f64,
beta: f64,
num_steps: usize,
) -> impl Fn(&Complex<f64>) -> Complex<f64> {
let leverage_cf = crate::affine_process::cir_leverage_jump(
move |u: &Complex<f64>| gamma_cf(u, alpha, beta),
t,
v0,
correlation,
alpha * beta,
a,
sigma,
lambda,
num_steps,
);
move |u: &Complex<f64>| leverage_cf(&u).exp()
}
#[cfg(test)]
mod tests {
use super::*;
use approx::*;
#[test]
fn test_gamma_leverage_expectation() {
let t = 2.0;
let num_steps = 1024;
let v0 = 1.0;
let a = 0.4;
let sigma = 0.4;
let lambda = 100.0;
let correlation = 0.9;
let alpha = 2.0;
let beta = 4.0;
let x_min = 0.0;
let x_max = lambda * alpha * beta * beta * 5.0 * t;
let num_u: usize = 256;
let cf = gamma_leverage(t, v0, a, sigma, lambda, correlation, alpha, beta, num_steps);
let discrete_cf = fang_oost::get_discrete_cf(num_u, x_min, x_max, &cf);
let expectation = cf_dist_utils::get_expectation_discrete_cf(x_min, x_max, &discrete_cf);
assert_abs_diff_eq!(expectation, lambda * alpha * beta * t, epsilon = 0.00001);
}
#[test]
fn test_gamma_leverage_expectation_leq() {
let t = 2.0;
let num_steps = 1024;
let v0 = 0.9;
let a = 0.4;
let sigma = 0.4;
let lambda = 100.0;
let correlation = 0.9;
let alpha = 2.0;
let beta = 4.0;
let x_min = 0.0;
let x_max = lambda * alpha * beta * beta * 5.0 * t;
let num_u: usize = 256;
let cf = gamma_leverage(t, v0, a, sigma, lambda, correlation, alpha, beta, num_steps);
let discrete_cf = fang_oost::get_discrete_cf(num_u, x_min, x_max, &cf);
let expectation = cf_dist_utils::get_expectation_discrete_cf(x_min, x_max, &discrete_cf);
assert_eq!(expectation < lambda * alpha * beta * t, true);
}
#[test]
fn test_gamma_leverage_expectation_geq() {
let t = 2.0;
let num_steps = 1024;
let v0 = 1.1;
let a = 0.4;
let sigma = 0.4;
let lambda = 100.0;
let correlation = 0.9;
let alpha = 2.0;
let beta = 4.0;
let x_min = 0.0;
let x_max = lambda * alpha * beta * beta * 5.0 * t;
let num_u: usize = 256;
let cf = gamma_leverage(t, v0, a, sigma, lambda, correlation, alpha, beta, num_steps);
let discrete_cf = fang_oost::get_discrete_cf(num_u, x_min, x_max, &cf);
let expectation = cf_dist_utils::get_expectation_discrete_cf(x_min, x_max, &discrete_cf);
assert_eq!(expectation > lambda * alpha * beta * t, true);
}
}