schwartz97distrstate: Schwartz two-factor Model: Distribution of the State...
In schwartz97: A package on the Schwartz two-factor commodity model

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.

## 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 `x` is a matrix, each row is taken to be a quantile.
`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 `numeric` representing the initial value of the commodity spot price or an object inheriting from class `schwartz2f`.
`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 `qmvnorm` of package `mvtnorm`.
`...`	Further arguments to be passed to methods of package `mvtnorm`.

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.

# ## 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")