Main Content

Simulation

Generate standard Monte Carlo and Quasi-Monte Carlo simulations from SDE models

Objects

sdeStochastic Differential Equation (SDE) model
bmBrownian motion (BM) models
gbmGeometric Brownian motion (GBM) model
merton Merton jump diffusion model
bates Bates stochastic volatility model
driftDrift-rate model component
diffusionDiffusion-rate model component
sdeddoStochastic Differential Equation (SDEDDO) model from Drift and Diffusion components
sdeldSDE with Linear Drift (SDELD) model
cevConstant Elasticity of Variance (CEV) model
cirCox-Ingersoll-Ross (CIR) mean-reverting square root diffusion model
hestonHeston model
hwvHull-White/Vasicek (HWV) Gaussian Diffusion model
sdemrdSDE with Mean-Reverting Drift (SDEMRD) model

Functions

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simBySolutionSimulate approximate solution of diagonal-drift GBM processes
simBySolutionSimulate approximate solution of diagonal-drift HWV processes
simBySolutionSimulate approximate solution of diagonal-drift Merton jump diffusion process
simByTransitionSimulate Heston sample paths with transition density
simByTransitionSimulate Bates sample paths with transition density
simByTransitionSimulate CIR sample paths with transition density
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme
simByEulerEuler simulation of stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, or SDEMRD models
simByEulerSimulate Bates sample paths by Euler approximation
simByEulerSimulate Merton jump diffusion sample paths by Euler approximation
simulateSimulate multivariate stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, SDEMRD, Merton, or Bates models
simulateSimulate multivariate stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, SDEMRD, Merton, or Bates models
simByEulerEuler simulation of stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, or SDEMRD models
interpolateBrownian interpolation of stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, or SDEMRD models
simByTransitionSimulate Heston sample paths with transition density
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme
simByTransitionSimulate CIR sample paths with transition density
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme
simBySolutionSimulate approximate solution of diagonal-drift GBM processes
simBySolutionSimulate approximate solution of diagonal-drift HWV processes
simulateSimulate multivariate stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, SDEMRD, Merton, or Bates models
simByEulerSimulate Bates sample paths by Euler approximation
simByTransitionSimulate Bates sample paths with transition density
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme
simulateSimulate multivariate stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, SDEMRD, Merton, or Bates models
simByEulerSimulate Merton jump diffusion sample paths by Euler approximation
simBySolutionSimulate approximate solution of diagonal-drift Merton jump diffusion process
ts2funcConvert time series arrays to functions of time and state

Examples and How To

Concepts

  • SDEs

    Model dependent financial and economic variables by performing standard Monte Carlo or Quasi-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.

  • Quasi-Monte Carlo Simulation

    Quasi-Monte Carlo simulation is a Monte Carlo simulation but uses quasi-random sequences instead pseudo random numbers.

  • Performance Considerations

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