Struct GeometricBrownianMotion 

pub struct GeometricBrownianMotion {
    pub s0: f64,
    pub mu: f64,
    pub sigma: f64,
    /* private fields */
}

Geometric Brownian Motion (GBM) for log-normal asset/particle dynamics.

SDE: dS = mu * S * dt + sigma * S * dW Exact solution: S(t) = S0 * exp((mu - sigma^2/2)t + sigmaW(t))

Fields

s0: f64

Initial value S(0).

mu: f64

Drift coefficient mu.

sigma: f64

Volatility coefficient sigma.

Implementations

impl GeometricBrownianMotion

pub fn new(s0: f64, mu: f64, sigma: f64, seed: u64) -> Self

Creates a new GBM process.

pub fn exact_path(&self, t_end: f64, n_steps: usize) -> Vec<f64>

Exact path using the analytical solution (no discretisation error).

Returns n_steps + 1 values including S(0) = s0.

pub fn euler_path(&self, t_end: f64, n_steps: usize) -> Vec<f64>

Euler-Maruyama discretisation path.

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

Theoretical mean E[S(t)] = S0 * exp(mu * t).

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

Theoretical variance Var[S(t)] = S0^2 * exp(2mut) * (exp(sigma^2*t) - 1).