Simulation

Generate Monte Carlo simulations from SDE models

Objects

`sde`	Stochastic Differential Equation (SDE) model
`bm`	Brownian motion models
`gbm`	Geometric Brownian motion model
`merton`	Merton jump diffusion model
`bates`	Bates stochastic volatility 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

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For sde, bm, gbm, cev, cir, hwv, heston, sdeddo, sdeld, or sdemrd models

`simulate`	Simulate multivariate stochastic differential equations (SDEs)
`simByEuler`	Euler simulation of stochastic differential equations (SDEs)
`interpolate`	Brownian interpolation of stochastic differential equations

For heston models

`simByTransition`	Simulate Heston sample paths with transition density
`simByQuadExp`	Simulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme

For cir models

`simByTransition`	Simulate Cox-Ingersoll-Ross sample paths with transition density
`simByQuadExp`	Simulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme

For gbm models

simBySolution Simulate approximate solution of diagonal-drift GBM processes

For hwv models

simBySolution Simulate approximate solution of diagonal-drift HWV processes

For bates models

`simulate`	Simulate multivariate stochastic differential equations (SDEs)
`simByEuler`	Simulate Bates sample paths by Euler approximation
`simByTransition`	Simulate Bates sample paths with transition density
`simByQuadExp`	Simulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme

For merton models

`simulate`	Simulate multivariate stochastic differential equations (SDEs)
`simByEuler`	Simulate Merton jump diffusion sample paths by Euler approximation
`simBySolution`	Simulate approximate solution of diagonal-drift Merton jump diffusion process

Conversion for time series arrays to functions of time and state

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™.