Black-Scholes-Merton Path Simulation
This application simulates a single path of a stock price using Black-Scholes-Merton (BSM) process. This process is formulated as a stochastic differential equation of the form \[ d\ln(S) = \left\{r(t)-q(t)-\frac{\sigma^2(t,S)}{2}\right\}dt + \sigma dW_t\] where $S_t$ is the stock price at time $t$, $r$ is the continuous risk-free rate of interest, $q$ is a continuous dividend yield, $\sigma$ is the volatility, and $dW_t$ is a Wiener process.
This application requires the following input data.
- starting price $S_0$, and $r,q,\sigma$
- 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.