fOptions (version 251.70)

EBMAsianOptions: Exponential Brownian Motion Distributions

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:

ll{ 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. }

ll{ 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. }

ll{ ZhangAsianOption Asian option price by Zhang's 1D PDE, VecerAsianOption Asian option price by Vecer's 1D PDE. }

ll{ 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. }

ll{ 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. }

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

ll{ 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. } Sorry - The Documentation is still Uncomplete.

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.

Examples

## Examples:
   # none ...