Documentation

# Simulation

Generate Monte Carlo simulations from SDE models

## Objects

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

## Functions

 `simulate` Simulate multivariate stochastic differential equations (SDEs) `simByEuler` Euler simulation of stochastic differential equations (SDEs) `simByTransition` Simulate Cox-Ingersoll-Ross sample paths with transition density `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 `ts2func` Convert 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.

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