Description Usage Arguments Value Examples

The geometric Ornstein-Uhlenbeck process is a member of the general affine class of stochastic process. The Ornstein-Uhlenbeck process is a Gaussian process, a Markov process, is temporally homogeneous and exhibits mean-reverting behaviour.
The `IGBM_simulate`

function utilizes antithetic variates as a simple variance reduction technique.

1 | ```
GOU_simulate(n, t, reversion_rate, sigma, equilibrium, risk_premium, S0, dt)
``` |

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

`t` |
The forecasting period, in years |

`reversion_rate` |
The reversion rate term of the GOU process |

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

`equilibrium` |
The equilibrium term of the GOU process |

`risk_premium` |
The risk premium of the GOU process |

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

`dt` |
The discrete time step of observations, in years A stochastic process S(t) is an IGBM that follows the following continuous-time stochastic differential equation:
Where 'reversion_rate' is the rate of reversion term, 'equilibrium' is the equilibrium value the process reverts towards, 'risk_premium' is the risk premium of the process, |

A matrix of simulated price paths of the GOU 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 8 9 | ```
## 100 simulations of 1 year of monthly price paths:
Simulated <- GOU_simulate(n = 100,
t = 1,
reversion_rate = 1,
sigma = 0.2,
equilibrium = 100,
risk_premium = 0.05,
S0 = 100,
dt = 1/12)
``` |

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