Description Usage Arguments Value Note Author(s) References See Also Examples

The definition of the process used here is:

dX_t = -a(X_t - mu) + sd*dW_t,

where (mu, a, sd) are the three real parameters.

1 2 3 4 |

`n` |
integer, number of paths. |

`m` |
integer, number of steps, the step size will be T/m. |

`x` |
double, the vector of the observed values of a Vasicek process. |

`x0` |
double, the initial value. |

`mu` |
double, the value on which the process is centered and has an attraction when it is away. |

`a` |
double, the coefficient of how strong is the mean reversion when the process is away from |

`sd` |
double, the volatility. |

`T` |
double, the final date on which the brownian motion is simulated. |

`drop` |
logical, if |

`log` |
logical, if TRUE, returns the log-density, if FALSE, returns the density. |

`a0` |
double, starting value of |

`rvasicek`

returns a `(n, m+1)`

matrix of n path of the Vasicek process. `dvasicek`

returns a vector of size `length(x)-1`

. Note that the first value has no density. `lvasicek`

returns the log-liklihood associated to `dvasicek`

and `evasicek`

returns the Maximum Likelihood Estimator of the parameters `(mu, a, sd)`

.

If `mu = 0`

, the process coincides with the Ornstein-Uhlenbeck process.

Nicolas Baradel - PGM Solutions

https://en.wikipedia.org/wiki/Vasicek_model

https://pgm-solutions.com/packages

1 2 |

```
[1] 0.6621352 1.0899338 1.2677005 1.1900134 0.7833885 0.4952588 1.3187989
[8] 1.0308698 1.3115995 0.7758035
```

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