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Last data update: 2014.03.03

R: Schwartz two-factor Model: Filter futures data

filter-futures

R Documentation

Schwartz two-factor Model: Filter futures data

Description

Filter a series of futures prices to obtain state variables.

Usage


## S4 method for signature 'ANY,ANY,numeric'
filter.schwartz2f(data, ttm, s0 = 50, delta0 = 0,
                  mu = 0.1, sigmaS = 0.3, kappa = 1, alpha = 0, sigmaE = 0.5,
                  rho = 0.75, r = 0.05, lambda = 0, alphaT = NULL,
                  deltat = 1/260, meas.sd = rep(1e-3, ncol(data)),
                  P0 = 0.5 * diag(c(log(s0), abs(delta0))))

## S4 method for signature 'ANY,ANY,schwartz2f'
filter.schwartz2f(data, ttm, s0,
                  r = 0.05, lambda = 0, alphaT = NULL, deltat = 1/260,
                  meas.sd = rep(1e-3, ncol(data)),
                  P0 = 0.1 * diag(2))

## S4 method for signature 'ANY,ANY,schwartz2f.fit'
filter.schwartz2f(data, ttm, s0)

Arguments

`data`	A matrix with futures prices.
`ttm`	A matrix with the corresponding time to maturity (see Details).
`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.
`r`	Instantaneous risk-free interest rate.
`lambda`	Market price of convenience yield risk.
`alphaT`	Mean-level of the convenience yield process with respect to the equivalent martingale measure.
`deltat`	Time increment.
`meas.sd`	The standard deviation of the measurement equation (see Details section of `fit.schwartz2f`).
`P0`	Variance of the state variables `s0` and `P0`.

Details

The elements of data and ttm have the following interpretation: data[i,j] denotes the futures price whose time to maturity was ttm[i,j] when it was observed. The unit of ttm is defined by deltat.

deltat is the time between observation data[i,j] and data[i + 1,j]. It is assumed to be constant, i.e., that data is a regular time-series.

Value

A list with components:

`state`	A matrix with `colnames` are “S” and “delta” giving the the expected spot price and the convenience yield.
`fkf.obj`	The filter output from the package `fkf`. Note that the log of the commodity spot price is filtered.

Author(s)

Philipp Erb, David Luethi, Juri Hinz

References

The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging by Eduardo S. Schwartz
Journal of Finance 52, 1997, 923-973

Examples

# data(futures)
# 
# ## Estimate parameters for coffee data (stop after 20 iterations)
# fit.obj <- fit.schwartz2f(futures$coffee$price, futures$coffee$ttm / 260,
#                           deltat = 1 / 260, control = list(maxit = 20))
# 
# ## Filter the futures data to get the spot price and the convenience yield.
# filtered <- filter.schwartz2f(futures$coffee$price, futures$coffee$ttm / 260, fit.obj)
# 
# ## ...and plot it.
# par(mfrow = c(2, 1))
# plot(filtered$state[,1], ylab = "Spot price", type = "l")
# lines(futures$coffee$price[,1], col = "red") # Closest to maturity futures
# plot(filtered$state[,2], ylab = "Convenience yield", type = "l")
# abline(h = 0)