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Last data update: 2014.03.03

R: Schwartz two-factor Model: Sampling from the State Variables

rand-state

R Documentation

Schwartz two-factor Model: Sampling from the State Variables

Description

Random number and trajectory generation of the state variables. The state variables are the commodity spot price s0 and the spot convenience yield delta0. The commodity log spot price and the convenience yield follow a bivariate normal distribution.

Usage


## S4 method for signature 'ANY,ANY,numeric'
rstate(n, time = 1, s0 = 50, delta0 = 0,
       mu = 0.1, sigmaS = 0.3, kappa = 1, alpha = 0,
       sigmaE = 0.5, rho = 0.75, method = "chol")

## S4 method for signature 'ANY,ANY,schwartz2f'
rstate(n, time = 1, s0, method = "chol")

## S4 method for signature 'ANY,ANY,numeric'
simstate(n, time = 1, s0 = 50, delta0 = 0,
         mu = 0.1, sigmaS = 0.3, kappa = 1, alpha = 0,
         sigmaE = 0.5, rho = 0.75, method = "chol")

## S4 method for signature 'ANY,ANY,schwartz2f'
simstate(n, time = 1, s0, method = "chol")

Arguments

`n`	Number of observations.
`time`	at which random numbers of the state variables are drawn (`rstate`) or horizon of the trajectory (`simstate`) relative to now.
`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.
`method`	See `rmvnorm` of package `mvtnorm`.

Details

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, qmvnorm and rmvnorm of the package mvtnorm.

Value

Samples or trajectories of the commodity spot price and instantaneous spot convenience yield as matrix.

Author(s)

Philipp Erb, David Luethi, Juri Hinz

Examples

# ## Create a "schwartz2f"-object
# model <- schwartz2f()
# 
# ## and sample from its distribution at time = 2.5.
# sim <- rstate(n = 1000, s0 = model, time = 2.5)
# par(mfrow = c(1, 2))
# hist(sim[,1], main = "Distribution of Spot Price")
# hist(sim[,2], main = "Distribution of Convenience Yield")
# 
# 
# ## Create a trajectory over a 6 years horizon sampled on a weekly basis.
# trajectory <- simstate(6 * 52, time = 6, s0 = model)
# par(mfrow = c(1, 2))
# plot(trajectory[,1], main = "Spot Price", type = "l")
# plot(trajectory[,2], main = "Convenience Yield", type = "l")