Ornstein-Uhlenbeck Path Simulation
This application simulates a single path of the Ornstein-Uhlenbeck process $X_t$. This process is formulated as a stochastic differential equation of the form \[ dX_t = \theta(\mu - X_t)dt + \sigma dW_t\] where $X_t$ is the stochastic process at time $t$, $\mu$ is the long-term mean, $\theta$ is the rate of mean reversion, $\sigma$ is the volatility, and $dW_t$ is a Wiener process.
This application requires the following input data.
- starting value $X_0$, and constants $\theta$, $\mu$, $\sigma$
- 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 $\Delta t=T/n$ 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.