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Simulation

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

Use SDE model objects with functions for standard Monte Carlo simulations and quasi-Monte Carlo simulations.

Objects

sdeStochastic Differential Equation (SDE) model
bmBrownian motion (BM) models
gbmGeometric Brownian motion (GBM) model
merton Merton jump diffusion model (Since R2020a)
bates Bates stochastic volatility model (Since R2020a)
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
rvmRough volatility model (RVM) (Since R2023b)
roughbergomiRough Bergomi model (Since R2024a)
roughhestonRough Heston model (Since R2024b)

Functions

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simByEulerEuler simulation of stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, or SDEMRD models
simByMilsteinSimulate diagonal diffusion for BM, GBM, CEV, HWV, SDEDDO, SDELD, or SDEMRD sample paths by Milstein approximation (Since R2023a)
simByMilstein2Simulate BM, GBM, CEV, HWV, SDEDDO, SDELD, SDEMRD process sample paths by second order Milstein approximation (Since R2023b)
simulateSimulate multivariate stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, SDEMRD, Merton, or Bates models
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 (Since R2020a)
simByTransitionSimulate Heston sample paths with transition density (Since R2020b)
simByTransitionSimulate Bates sample paths with transition density (Since R2020b)
simByTransitionSimulate CIR sample paths with transition density
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme (Since R2020a)
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 (Since R2020a)
simByEulerSimulate Merton jump diffusion sample paths by Euler approximation (Since R2020a)
simByMilsteinSimulate diagonal diffusion Merton sample paths by Milstein approximation (Since R2023a)
simByMilsteinSimulate Heston process sample paths by Milstein approximation (Since R2023a)
simByMilsteinSimulate Bates process sample paths by Milstein approximation (Since R2023a)
simByMilsteinSimulate CIR process sample paths by Milstein approximation (Since R2023a)
simByMilstein2Simulate Bates process sample paths by second order Milstein approximation (Since R2023b)
simByMilstein2Simulate CIR process sample paths by second order Milstein approximation (Since R2023a)
simByMilstein2Simulate Heston process sample paths by second order Milstein approximation (Since R2023b)
simByMilstein2Simulate diagonal diffusion Merton sample paths by second order Milstein approximation (Since R2023b)
simulateSimulate multivariate stochastic differential equations (SDEs) for SDE, BM, GBM, CEV, CIR, HWV, Heston, SDEDDO, SDELD, SDEMRD, Merton, or Bates models
simByEulerSimulate RVM, roughbergomi, or roughheston sample paths by Euler approximation (Since R2023b)
simByHybridSimulate RVM or roughbergomi sample paths by hybrid approximation (Since R2023b)
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 (Since R2020b)
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme (Since R2020a)
simByTransitionSimulate CIR sample paths with transition density
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme (Since R2020a)
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 (Since R2020a)
simByTransitionSimulate Bates sample paths with transition density (Since R2020b)
simByQuadExpSimulate Bates, Heston, and CIR sample paths by quadratic-exponential discretization scheme (Since R2020a)
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 (Since R2020a)
simBySolutionSimulate approximate solution of diagonal-drift Merton jump diffusion process (Since R2020a)
simByEulerSimulate RVM, roughbergomi, or roughheston sample paths by Euler approximation (Since R2023b)
simByHybridSimulate RVM or roughbergomi sample paths by hybrid approximation (Since R2023b)
ts2funcConvert time series arrays to functions of time and state

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