Description Usage Arguments Details Value Author(s) See Also Examples
Density, distribution function and quantile function of the state
variables. The state variables are the commodity spot price s
and the spot convenience yield delta
. The commodity log spot
price and the convenience yield follow a bivariate normal
distribution.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ## S4 method for signature 'ANY,ANY,numeric'
dstate(x, time = 1, s0 = 50, delta0 = 0,
mu = 0.1, sigmaS = 0.3, kappa = 1, alpha = 0,
sigmaE = 0.5, rho = 0.75, ...)
## S4 method for signature 'ANY,ANY,schwartz2f'
dstate(x, time = 1, s0, ...)
## S4 method for signature 'ANY,ANY,ANY,numeric'
pstate(lower, upper, time = 1, s0 = 50, delta0 = 0,
mu = 0.1, sigmaS = 0.3, kappa = 1, alpha = 0,
sigmaE = 0.5, rho = 0.75, ...)
## S4 method for signature 'ANY,ANY,ANY,schwartz2f'
pstate(lower, upper, time = 1, s0, ...)
## S4 method for signature 'ANY,ANY,numeric'
qstate(p, time = 1, s0 = 50, delta0 = 0,
mu = 0.1, sigmaS = 0.3, kappa = 1, alpha = 0,
sigmaE = 0.5, rho = 0.75, tail = "lower.tail", ...)
## S4 method for signature 'ANY,ANY,schwartz2f'
qstate(p, time = 1, s0, tail = "lower.tail", ...)
|
x |
Vector or matrix of quantiles. If |
time |
Time at which the quantity is computed (relative to time zero). |
p |
Probability, a scalar. |
lower |
The vector of lower limits of length 2. Note that first component stands for lower limit of the commodity spot price rather than the log-price. |
upper |
The vector of upper limits of length 2. Note that first component stands for the upper limit of the commodity spot price rather than the log-price. |
s0 |
Either a |
delta0 |
Initial value of the convenience yield. |
mu |
enters the drift of the commodity spot price. |
sigmaS |
Diffusion parameter of the spot price-process. |
kappa |
Speed of mean-reversion of the convenience yield process. |
alpha |
Mean-level of the convenience yield process. |
sigmaE |
Diffusion parameter of the convenience yield process. |
rho |
Correlation coefficient between the Brownian motion driving the spot price and the convenience yield process. |
tail |
See |
... |
Further arguments to be passed to methods of package
|
The model and its parameters are described in the Details
section of the schwartz2f
-class
documentation and in the package vignette Technical Document.
The above methods rely on the functions
pmvnorm
,
dmvnorm
, and
qmvnorm
of the package
mvtnorm
.
dstate
and pstate
return a numeric
, qstate
returns the output of qmvnorm
as a list
.
Philipp Erb, David Luethi, Juri Hinz
schwartz2f
-class description,
rstate
and simstate
for random number
generation, constructors schwartz2f
and
fit.schwartz2f
.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ## Create a "schwartz2f"-object
model <- schwartz2f()
## Probability
pstate(lower = c(0, -Inf), upper = c(45, 0.01), time = 1, model)
## Density
dstate(x = c(50, 0.03), time = 2, model)
dstate(x = rbind(c(50, 0.03), c(50, 0.1)), time = 2, model) # x is a matrix
## Quantile
qstate(p = 0.5, s0 = model)
## Generate random numbers
object <- schwartz2f(alpha = 0.05)
samples <- rstate(1000, time = 2, object)
## ...and plot histograms
par(mfrow = c(2, 1))
hist(samples[,1])
abline(v = mean(object, time = 2)[1], col = "red")
hist(samples[,2])
abline(v = mean(object, time = 2)[2], col = "red")
|
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