Simulation

Generate Monte Carlo simulations from SDE models

Objects

sdeStochastic Differential Equation (SDE) model
bmBrownian motion models
gbmGeometric Brownian motion model
driftDrift-rate model component
diffusionDiffusion-rate model component
sdeddoStochastic Differential Equation (SDE) model from Drift and Diffusion components
sdeldSDE with Linear Drift model
cevConstant Elasticity of Variance (CEV) model
cirCox-Ingersoll-Ross mean-reverting square root diffusion model
hestonHeston model
hwvHull-White/Vasicek Gaussian Diffusion model
sdemrdSDE with Mean-Reverting Drift model

Functions

simulateSimulate multivariate stochastic differential equations (SDEs)
simByEulerEuler simulation of stochastic differential equations (SDEs)
simByTransitionSimulate Cox-Ingersoll-Ross sample paths with transition density
simBySolutionSimulate approximate solution of diagonal-drift GBM processes
simBySolutionSimulate approximate solution of diagonal-drift HWV processes
interpolateBrownian interpolation of stochastic differential equations
ts2funcConvert time series arrays to functions of time and state

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.