Struct VarianceGammaProcess 

pub struct VarianceGammaProcess {
    pub mu: f64,
    pub sigma: f64,
    pub nu: f64,
}

The Variance-Gamma process: X_t = μ G_t + σ W_{G_t} where G_t is a Gamma process (subordinator) and W is a Brownian motion.

VG is a popular model in mathematical finance (Madan-Seneta model).

Fields

mu: f64

Drift parameter μ (asymmetry).

sigma: f64

Volatility parameter σ.

nu: f64

Variance rate ν of the Gamma subordinator.

Implementations

impl VarianceGammaProcess

pub fn new(mu: f64, sigma: f64, nu: f64) -> Self

Create a VG process with parameters (μ, σ, ν).

pub fn simulate( &self, x0: f64, t_end: f64, n_steps: u32, seed: u64, ) -> Vec<(f64, f64)>

Simulate a VG path starting at x0 over [0, t_end] with n_steps steps.

At each step, sample dG ~ Gamma(dt/ν, 1/ν), then X += μ dG + σ √(dG) Z.

pub fn theoretical_mean(&self, x0: f64, t: f64) -> f64

Theoretical mean of X_t: E[X_t] = x0 + μ t.

pub fn theoretical_variance(&self, t: f64) -> f64

Theoretical variance of X_t: Var[X_t] = σ² t + μ² ν t.

pub fn characteristic_exponent(&self, u: f64) -> f64

The VG characteristic exponent ψ(u) = log E[e^{iuX_1}].