EBMAsianOptions: Exponential Brownian Motion Distributions

In fAsianOptions: Rmetrics - EBM and Asian Option Valuation

Description

A collection and description of functions used in the theory of exponential Brownian Motion and in the valuation of Asian options.

The functions for Moment matching and Series Expansions are:

MomentMatchedAsianOption	Valuate moment matched option prices,
... method="LN"	Log-Normal Approximation of Levy, Turnbull and Wakeman,
... method="RG"	Reciprocal-Gamma Approximation of Milevski and Posner,
... method="JI"	Johnson Type I Approximation of Posner and Milevsky,
MomentMatchedAsianDensity	Valuate moment matched option densities,
... method="LN"	Log-Normal Approximation,
... method="RG"	Reciprocal-Gamma Approximation,
... method="JI"	Johnson Type I Approximation,
GramCharlierAsianOption	Calculate Gram-Charlier option prices.

AsianOptionMoments	Methods to calculate Asian Moments,
... method="A"	Moments from Abrahamson's Formula,
... method="D"	Moments from Dufresne's Formula,
... method="TW"	First 2 Moments from Turnbull-Wakeman,
... method="T"	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	Lower and upper bonds on Asian calls,
CurranThompsonAsianOption	From Thompson's continuous limit,
RogerShiThompsonAsianOption	From Thompson's single integral formula,
ThompsonAsianOption	Thompson's upper bound,
TolmatzAsianOption	Lower Bound from Tolmatz' symptotics.

CallPutParityAsianOption	Call-Put parity Relation,
WithDividendsAsianOption	Adds dividends to Asian option formula.

FuMadanWangTable	Table from Fu, Madan and Wang's paper,
FusaiTaglianiTable	Table from Fusai und tagliani's paper,
GemanTable	Table from Geman's paper,
LinetzkyTable	Table from Linetzky's paper,
ZhangTable	Table from Zhang's paper,
ZhangLongTable	Long Table from Zhang's paper,
ZhangShortTable	Short Table from Zhang's paper.

Usage

MomentMatchedAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30, table = NA, method = c("LN", "RG", "JI"))
MomentMatchedAsianDensity(x, Time = 1, r = 0.09, sigma = 0.30, 
    method = c("LN", "RG", "JI"))
GramCharlierAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30, table = NA, method = c("LN", "RG", "JI"))

AsianOptionMoments(M = 4, Time = 1, r = 0.045, sigma = 0.30, log = FALSE, 
    method = c("A", "D", "TW", "T"))








ZhangAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30, table = NA, correction = TRUE, nint = 800, 
    eps = 1.0e-8, dt = 1.0e-10)
VecerAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30, table = NA, nint = 800, eps = 1.0e-8, 
    dt = 1.0e-10)  

gGemanYor(lambda, S = 100, X = 100, Time = 1, r = 0.05, sigma = 0.30, 
    log = FALSE, doplot = FALSE)
GemanYorAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30, doprint = FALSE)
gLinetzky(x, y, tau, nu, ip = 0)
LinetzkyAsianOption(TypeFlag = c("c", "p"), S = 2, X = 2, Time = 1, 
    r = 0.02, sigma = 0.1, table = NA, lower = 0, upper = 100, 
    method = "adaptive", subdivisions = 100, ip = 0, doprint = TRUE, 
    doplot = TRUE, ...)

BoundsOnAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30, table = NA, method = c("CT", "RST", "T"))
CurranThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, 
    Time = 1, r = 0.09, sigma = 0.30)
RogerShiThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, 
    Time = 1, r = 0.09, sigma = 0.30)   
ThompsonAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30)
TolmatzAsianOption(TypeFlag = c("c", "p"), S = 100, X = 100, Time = 1, 
    r = 0.09, sigma = 0.30)

CallPutParityAsianOption(TypeFlag = "p", Price = 8.828759, S = 100, 
    X = 100, Time = 1, r = 0.09, sigma = 0.3, table = NA)
WithDividendsAsianOption(TypeFlag = "c", Dividends = 0.45, S = 100, 
    X = 100, Time = 1, r = 0.09, sigma = 0.3, 
    calculator = MomentMatchedAsianOption, method = "LN")

FuMadanWangTable()
FusaiTaglianiTable()
GemanTable()
LinetzkyTable()
ZhangTable()
ZhangLongTable()
ZhangShortTable()

Arguments

calculator	[WithDividendsAsianOption] - the name of the function selecting the option calculator to be used.
correction	[ZhangAsianOption] - xxx.
Dividends	[WithDividendsAsianOption] - xxx.
doplot	[gGemanYor][LinetzkyAsianOption] - xxx.
doprint	[GemanYorAsianOption][LinetzkyAsianOption] - xxx.
dt	[VecerAsianOption][ZhangAsianOption] - xxx.
eps	[VecerAsianOption][ZhangAsianOption] - xxx.
ip	[gLinetzky] - xxx.
lambda	[gGemanYor] - xxx.
log	[AsianOptionMoments][gGemanYor] - xxx.
lower, upper	[LinetzkyAsianOption] - xxx.
M	[*] - xxx.
method	[*] - xxx.
nint	[*] - xxx.
nu	[*] - xxx.
Price	[*] - xxx.
r	a numeric value, the annualized rate of interest; e.g. 0.25 means 25% pa.
S	the asset price, a numeric value.
sigma	a numeric value, the annualized volatility of the underlying security; e.g. 0.3 means 30% volatility pa.
subdivisions	[*] - xxx.
table	[*] - xxx.
tau	[*] - xxx.
Time	a numeric value, the time to maturity measured in years; e.g. 0.5 means 6 months.
TypeFlag	a character string either "c" for a call option or a "p" for a put option.
x	[*] - xxx.
X	a numeric value, the exercise price.
y	[*] - xxx.
...	[*] - xxx.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

Examples

## Examples:
   # none ...

fAsianOptions documentation built on May 2, 2019, 8:19 a.m.