Geometric Brownian Motion Path Simulation
This application simulates a single path of a stock price using geometric Brownian motion (GBM). The GBM process can be formulated as a stochastic differential equation of the form \[ dS_t = \mu S_t dt + \sigma S_t dW_t\] where $S_t$ is the stock price at time $t$, $\mu$ is the constant drift or trend (annual return) of the process, $\sigma$ or stock's volatility is the random variation around the trend, and $dW_t$ is a Wiener process.
This application requires the following input data.
- starting price $S_0$, interest rate $\mu$, and volatility $\sigma$
- random seed, if left blank or the input is 0 the application assigns a positive integer to the random seed automatically.
- time length (year) $T$ and number of time steps (day) $n$ 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.