# Documentation

### This is machine translation

Translated by
Mouseover text to see original. Click the button below to return to the English verison of the page.

# Simulation

Generate Monte Carlo simulations from SDE models

## Classes

 `sde` Stochastic Differential Equation (SDE) model `bm` Brownian motion models `cev` Constant Elasticity of Variance (CEV) models `cir` Cox-Ingersoll-Ross mean-reverting square root diffusion models `diffusion` Diffusion-rate model component `drift` Drift-rate model component `gbm` Geometric Brownian motion model `heston` Heston model `hwv` Hull-White/Vasicek Gaussian Diffusion model `sdeddo` Stochastic Differential Equation (SDE) model from Drift and Diffusion components `sdeld` SDE with Linear Drift model `sdemrd` SDE with Mean-Reverting Drift model

## Functions

 `simulate` Simulate multivariate stochastic differential equations (SDEs) `simByEuler` Euler simulation of stochastic differential equations (SDEs) `simBySolution` Simulate approximate solution of diagonal-drift GBM processes `simBySolution` Simulate approximate solution of diagonal-drift HWV processes `interpolate` Brownian interpolation of stochastic differential equations

## Examples and How To

Simulating Equity Prices

This example compares alternative implementations of a separable multivariate geometric Brownian motion process.

Simulating Interest Rates

This example highlights the flexibility of refined interpolation by implementing this power-of-two algorithm.

Stratified Sampling

This example specifies a noise function to stratify the terminal value of a univariate equity price series.

Pricing American Basket Options by Monte Carlo Simulation

This example shows how to model the fat-tailed behavior of asset returns and assess the impact of alternative joint distributions on basket option prices.

Improving Performance of Monte Carlo Simulation with Parallel Computing

This example shows how to improve the performance of a Monte Carlo simulation using Parallel Computing Toolbox™.

## Concepts

SDEs

Model dependent financial and economic variables by performing Monte Carlo simulation of stochastic differential equations (SDEs).

SDE Models

Most models and utilities available with Monte Carlo Simulation of SDEs are represented as MATLAB® objects.

Performance Considerations

Performance considerations for managing memory when solving most problems supported by the SDE engine.