Description Usage Arguments Details Value Examples

GBM is a commonly used stochastic process to simulate the price paths of stock prices and other assets, in which the log of the asset follows a random walk process with drift.
The `GBM_simulate`

function utilizes antithetic variates as a simple variance reduction technique.

1 | ```
GBM_simulate(n, t, mu, sigma, S0, dt)
``` |

`n` |
The total number of price paths to simulate |

`t` |
The forecasting period, in years |

`mu` |
The drift term of the GBM process |

`sigma` |
The volatility term of the GBM process |

`S0` |
The initial value of the underlying asset |

`dt` |
The discrete time step of observations, in years |

A stochastic process S(t) is a geometric brownian motion that follows the following continuous-time stochastic differential equation:

*dS(t)/S(t) = mu dt + sigma dW(t)*

Where *'mu'* is the drift term, *'sigma'* the volatility term and *W(t)* is defined as a Weiner process.

The GBM is log-normally distributed.

A matrix of simulated price paths of the GBM process. Each column corresponds to a simulated price path, and each row corresponds to a simulated observed price of the simulated price paths at each discrete time period.

1 2 3 4 5 6 7 | ```
## 100 simulations of 1 year of monthly price paths:
Simulated <- GBM_simulate(n = 100,
t = 1,
mu = 0.05,
sigma = 0.2,
S0 = 100,
dt = 1/12)
``` |

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