# Basic Option Valuation

### Description

The Rmetrics "Options" package is a collection of functions to valuate basic pptions.

### Details

Package: | fOptions |

Type: | Package |

Version: | R 3.0.1 |

Date: | 2014 |

License: | GPL Version 2 or later |

Copyright: | (c) 1999-2014 Rmetrics Assiciation |

URL: | https://www.rmetrics.org |

### 1 Introduction

The `fOptions`

package provides function for pricing
and evaluationg basic options.

### 2 Plain Vanilla Option

This section provides a collection of functions to valuate plain vanilla options. Included are functions for the Generalized Black-Scholes option pricing model, for options on futures, some utility functions, and print and summary methods for options.

1 2 3 4 5 | ```
GBS* the generalized Black-Scholes option
BlackScholesOption a synonyme for the GBSOption
Black76Option options on Futures
MiltersenSchwartzOption options on commodity futures
``` |

1 2 | ```
NDF, CND, CBND distribution functions
``` |

1 2 3 |

### 3 Binomial Tree Options

This section offers a collection of functions to valuate options in the framework of the Binomial tree option approach.

1 2 3 4 5 6 | ```
CRRBinomialTreeOption CRR Binomial Tree Option
JRBinomialTreeOption JR Binomial Tree Option
TIANBinomialTreeOption TIAN Binomial Tree Option
BinomialTreeOption Binomial Tree Option
BinomialTreePlot Binomial Tree Plot
``` |

### 4 Monte Carlo Options

In this section we provide functions to valuate options by Monte Carlo methods. The functions include beside the main Monte Carlo Simulator, example functions to generate Monte Carlo price paths and to compute Monte Carlo price payoffs.

1 2 3 4 5 6 |

### 5 Low Discrepancy Sequences

This section provides three types of random number generators for univorm and normal distributed deviates. These area pseudo random number generator and a halton and sobol generator for low discrepancy sequences.

1 2 3 | ```
runif.pseudo Uniform pseudo random numbers
rnorm.pseudo Normal pseudo random numbers
``` |

1 2 3 | ```
runif.halton Uniform Halton sequence
rnorm.halton Normal Halton sequence
``` |

1 2 3 | ```
runif.sobol Uniform scrambled Sobol sequence
rnorm.sobol Normal scrambled Sobol sequence
``` |

r

### 6 Heston Nandi Garch Fit

Her we provide functions to model the GARCH(1,1) price paths which underly Heston and Nandi's option pricing model. The functions are:

1 2 3 4 | ```
hngarchSim simulates a Heston-Nandi Garch(1,1) process
hngarchFit fits parameters of a Heston Nandi Garch(1,1) model
``` |

1 2 | ```
hngarchStats returns true moments of the log-Return distribution
``` |

1 2 3 | ```
print.hngarch print method, \cr
summary.hngarch diagnostic summary
``` |

### 7 Heston Nandi Garch Options

This section comes with functions to valuate Heston-Nandi options. Provided are functions to compute the option price and the delta and gamma sensitivities for call and put options.

1 2 3 4 | ```
HNGOption Heston-Nandi GARCH(1,1) option price
HNGGreeks Heston-Nandi GARCH(1,1) option sensitivities
HNGCharacteristics combines option prices and sensitivities
``` |

### About Rmetrics

The `fOptions`

Rmetrics package is written for educational
support in teaching "Computational Finance and Financial Engineering"
and licensed under the GPL.