# Simulation

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

## Objects

`sde` | Stochastic Differential Equation (`SDE` ) model |

`bm` | Brownian motion (`BM` ) models |

`gbm` | Geometric Brownian motion (`GBM` ) model |

`merton` |
`Merton` jump diffusion model (Since R2020a) |

`bates` |
`Bates` stochastic volatility model (Since R2020a) |

`drift` | Drift-rate model component |

`diffusion` | Diffusion-rate model component |

`sdeddo` | Stochastic Differential Equation (`SDEDDO` ) model from Drift
and Diffusion components |

`sdeld` | SDE with Linear Drift (`SDELD` ) model |

`cev` | Constant Elasticity of Variance (`CEV` ) model |

`cir` | Cox-Ingersoll-Ross (`CIR` ) mean-reverting square root diffusion
model |

`heston` | `Heston` model |

`hwv` | Hull-White/Vasicek (`HWV` ) Gaussian Diffusion model |

`sdemrd` | SDE with Mean-Reverting Drift (`SDEMRD` ) model |

`rvm` | Rough volatility model (`RVM` ) (Since R2023b) |

`roughbergomi` | Rough Bergomi model (Since R2024a) |

`roughheston` | Rough Heston model (Since R2024b) |

## Functions

## Topics

**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.

**Price American Basket Options Using Standard Monte Carlo and Quasi-Monte Carlo Simulation**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™.

**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.