# 模拟

## 对象

 `sde` 随机微分方程 (`SDE`) 模型 `bm` 布朗运动 (`BM`) 模型 `gbm` 几何布朗运动 (`GBM`) 模型 `merton` `Merton` jump diffusion model (自 R2020a 起) `bates` `Bates` stochastic volatility model (自 R2020a 起) `drift` 漂移率模型分量 `diffusion` 扩散率模型分量 `sdeddo` 基于漂移和扩散分量建立随机微分方程 (`SDEDDO`) 模型 `sdeld` SDE with Linear Drift (`SDELD`) model `cev` 常方差弹性 (`CEV`) 模型 `cir` 考克斯-英格索尔-罗斯 (`CIR`) 均值回归平方根扩散模型 `heston` `Heston` 模型 `hwv` 赫尔-怀特/瓦西塞克 (`HWV`) 高斯扩散模型 `sdemrd` 采用均值回归漂移 (`SDEMRD`) 模型的 SDE `rvm` Rough volatility model (`RVM`) (自 R2023b 起) `roughbergomi` Rough Bergomi model (自 R2024a 起)

## 函数

 `simByEuler` Euler simulation of stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, or `SDEMRD` models `simByMilstein` Simulate diagonal diffusion for `BM`, `GBM`, `CEV`, `HWV`, `SDEDDO`, `SDELD`, or `SDEMRD` sample paths by Milstein approximation (自 R2023a 起) `simByMilstein2` Simulate `BM`, `GBM`, `CEV`, `HWV`, `SDEDDO`, `SDELD`, `SDEMRD` process sample paths by second order Milstein approximation (自 R2023b 起) `simulate` Simulate multivariate stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, `SDEMRD`, `Merton`, or `Bates` models
 `simBySolution` Simulate approximate solution of diagonal-drift `GBM` processes `simBySolution` Simulate approximate solution of diagonal-drift `HWV` processes `simBySolution` Simulate approximate solution of diagonal-drift `Merton` jump diffusion process (自 R2020a 起) `simByTransition` Simulate `Heston` sample paths with transition density (自 R2020b 起) `simByTransition` Simulate `Bates` sample paths with transition density (自 R2020b 起) `simByTransition` Simulate `CIR` sample paths with transition density `simByQuadExp` Simulate `Bates`, `Heston`, and `CIR` sample paths by quadratic-exponential discretization scheme (自 R2020a 起) `simByEuler` Euler simulation of stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, or `SDEMRD` models `simByEuler` Simulate `Bates` sample paths by Euler approximation (自 R2020a 起) `simByEuler` Simulate `Merton` jump diffusion sample paths by Euler approximation (自 R2020a 起) `simByMilstein` Simulate diagonal diffusion `Merton` sample paths by Milstein approximation (自 R2023a 起) `simByMilstein` Simulate `Heston` process sample paths by Milstein approximation (自 R2023a 起) `simByMilstein` Simulate `Bates` process sample paths by Milstein approximation (自 R2023a 起) `simByMilstein` Simulate `CIR` process sample paths by Milstein approximation (自 R2023a 起) `simByMilstein2` Simulate `Bates` process sample paths by second order `Milstein` approximation (自 R2023b 起) `simByMilstein2` Simulate `CIR` process sample paths by second order Milstein approximation (自 R2023a 起) `simByMilstein2` Simulate `Heston` process sample paths by second order Milstein approximation (自 R2023b 起) `simByMilstein2` Simulate diagonal diffusion `Merton` sample paths by second order Milstein approximation (自 R2023b 起) `simulate` Simulate multivariate stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, `SDEMRD`, `Merton`, or `Bates` models
 `simByEuler` Simulate `RVM`, `roughbergomi`, or `roughheston` sample paths by Euler approximation (自 R2023b 起) `simByHybrid` Simulate `RVM` or `roughbergomi` sample paths by hybrid approximation (自 R2023b 起)
 `simulate` Simulate multivariate stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, `SDEMRD`, `Merton`, or `Bates` models `simByEuler` Euler simulation of stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, or `SDEMRD` models `interpolate` Brownian interpolation of stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, or `SDEMRD` models
 `simByTransition` Simulate `Heston` sample paths with transition density (自 R2020b 起) `simByQuadExp` Simulate `Bates`, `Heston`, and `CIR` sample paths by quadratic-exponential discretization scheme (自 R2020a 起)
 `simByTransition` Simulate `CIR` sample paths with transition density `simByQuadExp` Simulate `Bates`, `Heston`, and `CIR` sample paths by quadratic-exponential discretization scheme (自 R2020a 起)
 `simBySolution` Simulate approximate solution of diagonal-drift `GBM` processes
 `simBySolution` Simulate approximate solution of diagonal-drift `HWV` processes
 `simulate` Simulate multivariate stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, `SDEMRD`, `Merton`, or `Bates` models `simByEuler` Simulate `Bates` sample paths by Euler approximation (自 R2020a 起) `simByTransition` Simulate `Bates` sample paths with transition density (自 R2020b 起) `simByQuadExp` Simulate `Bates`, `Heston`, and `CIR` sample paths by quadratic-exponential discretization scheme (自 R2020a 起)
 `simulate` Simulate multivariate stochastic differential equations (SDEs) for `SDE`, `BM`, `GBM`, `CEV`, `CIR`, `HWV`, `Heston`, `SDEDDO`, `SDELD`, `SDEMRD`, `Merton`, or `Bates` models `simByEuler` Simulate `Merton` jump diffusion sample paths by Euler approximation (自 R2020a 起) `simBySolution` Simulate approximate solution of diagonal-drift `Merton` jump diffusion process (自 R2020a 起)
 `ts2func` Convert time series arrays to functions of time and state