Ornstein-Uhlenbeck Multi-Path Simulation
This application simulates multiple paths of correlated Ornstein-Uhlenbeck processes.
The application requires the following input data.
- An $m\times 4$ matrix whose $k^{\text{th}}$ row contains $X_0,\theta,\mu,\sigma$ of the $k^{\text{th}}$ process, and $m$ is the number of processes in the simulation. See Ornstein-Uhlenbeck Path Simulation for the description of the parameters.
- An $m\times m$ Pearson correlation matrix, if this input is left blank, the paths are treated as not correlated or independent of each other. This matrix can be created using Correlation Matrix Calculator.
- random seed, if left blank or the input is 0 the application assigns a positive integer to the random seed automatically.
- time length $T$ and number of time steps $n$ so that the step size $\Delta t=T/n$ is used in the simulation.
- This simulation uses normally distributed random numbers which are generated using either inverse cumulative normal method or Box-Muller transformation method.