The Rmetrics "fAsianOptions" package is a collection of functions to analyze and model Exponential Brownian Motion and to valuate Asian options.
The fAsianOptions package provides functions for pricing
and valuating Asian Options together with tools for analyzing
and modeling Exponential Brownian Motion (EBM).
This is a collection of functions used in the theory of exponential Brownian Motion, EBM, and in the valuation of Asian options.
MomentMatchedAsianOption valuate moment matched option prices
- "LN" Log-Normal Approx of Levy, Turnbull and Wakeman
- "RG" Reciprocal-Gamma Approx of Milevski and Posner
- "JI" Johnson Type I Approx of Posner and Milevsky
MomentMatchedAsianDensity valuate moment matched option densities
- "LN" Log-Normal Approximation
- "RG" Reciprocal-Gamma Approximatio
- "JI" Johnson Type I Approximation
GramCharlierAsianOption calculates Gram-Charlier option prices
AsianOptionMoments methods to calculate Asian Moments
- "A" using moments from Abrahamson's Formula
- "D" using moments from Dufresne's Formula
- "TW" using first 2 Moments from Turnbull-Wakeman
- "T" including asymptotic Behavior after Tolmatz
ZhangAsianOption Asian option price by Zhang's 1D PDE
VecerAsianOption Asian option price by Vecer's 1D PDE
gGemanYor Function to be Laplace inverted
GemanYorAsianOption Asian option price by Laplace Inversion
gLinetzky Function to be integrated
LinetzkyAsianOption Asian option price by Spectral Expansion
BoundsOnAsianOption using lower and upper bonds on Asian calls
CurranThompsonAsianOption using Thompson's continuous limit
RogerShiThompsonAsianOption using Thompson's single integral formula
ThompsonAsianOption using Thompson's upper bound
TolmatzAsianOption using lower bound from Tolmatz' asymptotics
CallPutParityAsianOption using Call-Put parity relation
WithDividendsAsianOption adding dividends to Asian option formula
FuMadanWangTable returns table from Fu, Madan and Wang's paper
FusaiTaglianiTable returns able from Fusai und tagliani's paper
GemanTable returns table from Geman's paper
LinetzkyTable returns table from Linetzky's paper
ZhangTable returns table from Zhang's paper
ZhangLongTable returns long table from Zhang's paper
ZhangShortTable returns short table from Zhang's paper
In this section we summarize distributions and related functions which are useful in the theory of exponential Brownian motion and Asian option valuation. The functions compute densities and probabilities for the log-Normal distribution, the Gamma distribution, the Reciprocal-Gamma distribution, and the Johnson Type-I distribution. Functions are made available for the compution of moments including the Normal, the log-Normal, the Reciprocal-Gamma, and the Asian-Option Density. In addition a function is given to compute numerically first and second derivatives of a given function.
dlognorm returns the log-Normal density and derivatives
plognorm returns the log-Normal, a synonyme for R's plnorm
dgam returns the Gamma density, a synonyme for R's dgamma
pgam returns the Gamma probability, a synonyme for R's pgamma
drgam returns the Reciprocal-Gamma density
prgam returns the Reciprocal-Gamma probability
djohnson returns the Johnson Type I density
pjohnson returns the Johnson Type I probability
mnorm returns the moments of Normal density
mlognorm returns the moments of log-Normal density
mrgam returns the moments of reciprocal-Gamma density
masian returns the moments of Asian Option density
derivative returns the first and second numerical derivative
This section offers special mathematical functions which compute the modified Bessel functions of integer order of the first and second kind as well as their derivatives.
BesselI computes modified Bessel function of the 1st kind
BesselDI computes its derivative
BesselK computes the modified Bessel function of the 3nd kind
BesselDK computes its derivative
This section offers special mathematical functions which compute the Gamma function and related functions. The functions include the error function, the Psi function, the incomplete Gamma function, the Gamma function for complex argument, and the Pochhammer symbol. The Gamma function the logarithm of the Gamma function, their first four derivatives, and the Beta function and the logarithm of the Beta function are part of R's base package (marked by an asterisk). For example, these functions are required to valuate Asian Options based on the theory of exponential Brownian motion.
erf computes the Error function
gamma* computes the Gamma function
lgamma* the logarithm of the Gamma function
digamma* the first derivative of the Log Gamma function
trigamma* the second derivative of the Log Gamma function
tetragamma* the third derivative of the Log Gamma function
pentagamma* the fourth derivative of the Log Gammafunction
beta* the Beta function
lbeta* the logarithm of the Beta function
Psi computes the Psi or Digamma function
igamma computes the incomplete Gamma function
cgamma computes the Gamma function for complex argument
Pochhammer returns the Pochhammer symbol
This section offers special mathematical functions which compute the confluent hypergeometric and related functions. These functions are required to valuate Asian Options based on the theory of exponential Brownian motion.
kummerM the Confluent Hypergeometric Function of the 1st kind
kummerU the Confluent Hypergeometric Function of the 2nd kind
whittakerM the Whittaker M Function
whittakerW the Whittaker W Function
hermiteH the Hermite Polynomials
The fOptions Rmetrics package is written for educational
support in teaching "Computational Finance and Financial Engineering"
and licensed under the GPL.
Package: \tab fAsianOptions\cr
Type: \tab Package\cr
Version: \tab R 3.0.1\cr
Date: \tab 2014\cr
License: \tab GPL Version 2 or later\cr
Copyright: \tab (c) 1999-2014 Rmetrics Association\cr
Repository: \tab R-FORGE\cr
URL: \tab \url{https://www.rmetrics.org}