Description Usage Arguments Details Value Author(s) References Examples

Density, distribution function, quantile function, and
random generation for the conditional law *X(t) | X(0) = x0*
of the Black-Scholes-Merton process
also known as the geometric Brownian motion process.

1 2 3 4 |

`x` |
vector of quantiles. |

`p` |
vector of probabilities. |

`Dt` |
lag or time. |

`x0` |
the value of the process at time |

`theta` |
parameter of the Black-Scholes-Merton process; see details. |

`n` |
number of random numbers to generate from the conditional distribution. |

`log, log.p` |
logical; if TRUE, probabilities |

`lower.tail` |
logical; if TRUE (default), probabilities are |

This function returns quantities related to the conditional law of the process solution of

*dX_t = theta[1]*Xt*dt + theta[2]*Xt*dWt.*

Constraints: *theta[3]>0*.

`x` |
a numeric vector |

Stefano Maria Iacus

Black, F., Scholes, M.S. (1973) The pricing of options
and corporate liabilities, *Journal of Political Economy*, 81, 637-654.

Merton, R. C. (1973) Theory of rational option pricing,
*Bell Journal of Economics and Management Science*, 4(1), 141-183.

1 |

```
Loading required package: MASS
Loading required package: stats4
Loading required package: fda
Loading required package: splines
Loading required package: Matrix
Attaching package: 'fda'
The following object is masked from 'package:graphics':
matplot
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
sde 2.0.15
Companion package to the book
'Simulation and Inference for Stochastic Differential Equations With R Examples'
Iacus, Springer NY, (2008)
To check the errata corrige of the book, type vignette("sde.errata")
[1] 1.066929
```

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