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.
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 (see
Details).
alphaT
Mean-level of the convenience yield process with
respect to the equivalent martingale measure (see Details).
Details
The model and its parameters are described in the Details
section of the schwartz2f-class
documentation and in the package vignette Technical Document.
Value
A numeric containing futures prices.
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
Valuation of Commodity Futures and Options under Stochastic
Convenience Yields, Interest Rates, and Jump Diffusions in the Spot
by Jimmy E. Hilliard and Jorge Reis Journal of Financial and
Quantitative Analysis 33, 1998, 61-86
See Also
priceoption to price options,
d/p/q/rfutures to work with futures,
schwartz2f-constructor,
fit.schwartz2f for parameter estimation,
futures-data.
Examples
# ## function call by atomic arguments
# forward.curve <- pricefutures(ttm = 0.2 * 1:10, s0 = 10, delta0 = 0,
# alpha = 0, lambda = 0.02, r = 0)
# plot(forward.curve, type = "b")
#
# ## function call via schwartz2f-object.
# obj <- schwartz2f(delta0 = 0, sigmaE = 1e-5) # Make convenience yield inactive
# forward.curve <- pricefutures(ttm = 0.2 * 1:10, s0 = obj, r = 0, alphaT = 0)
# plot(forward.curve, type = "b")