Module RustQuant::stochastics

Monte Carlo engines to simulate stochastic processes.

The following is a list of stochastic processes that can be generated.

• Brownian Motions:
  • Standard Brownian Motion
    • $dX(t) = dW(t)$
  • Arithmetic Brownian Motion
    • $dX(t) = \mu dt + \sigma dW(t)$
  • Geometric Brownian Motion
    • $dX(t) = \mu X(t) dt + \sigma X(t) dW(t)$
  • Fractional Brownian Motion
• Cox-Ingersoll-Ross (1985)
  • $dX(t) = \left[ \theta - \alpha X(t) \right] dt + \sigma \sqrt{r_t} dW(t)$
• Ornstein-Uhlenbeck process
  • $dX(t) = \theta \left[ \mu - X(t) \right] dt + \sigma dW(t)$
• Ho-Lee (1986)
  • $dX(t) = \theta(t) dt + \sigma dW(t)$
• Hull-White (1990)
  • $dX(t) = \left[ \theta(t) - \alpha X(t) \right]dt + \sigma dW(t)$
• Extended Vasicek (1990)
  • $dX(t) = \left[ \theta(t) - \alpha(t) X(t) \right] dt + \sigma dW(t)$
• Black-Derman-Toy (1990)
  • $d\ln[X(t)] = \left[ \theta(t) + \frac{\sigma’(t)}{\sigma(t)}\ln[X(t)] \right]dt + \sigma_t dW(t)$

use RustQuant::stochastics::*;
use RustQuant::models::*;

// Create new GBM with mu and sigma.
let gbm = GeometricBrownianMotion::new(0.05, 0.9);

// Generate path using Euler-Maruyama scheme.
// Parameters: x_0, t_0, t_n, n, sims, parallel.
let output = (&gbm).euler_maruyama(10.0, 0.0, 0.5, 10, 1, false);

println!("GBM = {:?}", output.paths);

Re-exports

• pub use process::*;

Modules

• arithmetic_brownian_motion
  Arithmetic Brownian Motion.
• black_derman_toy
  Black-Derman-Toy short rate model.
• brownian_motion
  Standard Brownian Motion.
• constant_elasticity_of_variance
  Constant Elasticity of Variance process.
• cox_ingersoll_ross
  Cox-Ingersoll-Ross process.
• extended_vasicek
  Extended Vasicek process.
• fractional_brownian_motion
  Fractional Brownian Motion.
• fractional_cox_ingersoll_ross
  Fractional Cox-Ingersoll-Ross process.
• fractional_ornstein_uhlenbeck
  Fractional Ornstein-Uhlenbeck process.
• geometric_brownian_bridge
  Geometric brownian bridge process.
• geometric_brownian_motion
  Geometric Brownian Motion.
• heston
  Heston model process.
• ho_lee
  Ho-Lee process.
• hull_white
  Hull-White model process.
• merton_jump_diffusion
  Merton jump diffusion process.
• ornstein_uhlenbeck
  Ornstein-Uhlenbeck process.
• process
  Defines Trajectories and StochasticProcess. Trajectories is the return type of all the stochastic processes. StochasticProcess is the base trait for all the stochastic processes.
• sabr
  SABR model process.