EBMAsianOptions | R Documentation |
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. |
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()
calculator |
[WithDividendsAsianOption] - |
correction |
[ZhangAsianOption] - |
Dividends |
[WithDividendsAsianOption] - |
doplot |
[gGemanYor][LinetzkyAsianOption] - |
doprint |
[GemanYorAsianOption][LinetzkyAsianOption] - |
dt |
[VecerAsianOption][ZhangAsianOption] - |
eps |
[VecerAsianOption][ZhangAsianOption] - |
ip |
[gLinetzky] - |
lambda |
[gGemanYor] - |
log |
[AsianOptionMoments][gGemanYor] - |
lower, upper |
[LinetzkyAsianOption] - |
M |
[*] - |
method |
[*] - |
nint |
[*] - |
nu |
[*] - |
Price |
[*] - |
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 |
[*] - |
table |
[*] - |
tau |
[*] - |
Time |
a numeric value, the time to maturity measured in years; e.g. 0.5 means 6 months. |
TypeFlag |
a character string either |
x |
[*] - |
X |
a numeric value, the exercise price. |
y |
[*] - |
... |
[*] - |
Diethelm Wuertz for the Rmetrics R-port.
## Examples: # none ...
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