Description Objects from the Class Slots Details Extends Author(s) References See Also Examples
The schwartz2f
class stores parameters which determine initial
values and the dynamics of the state variables. The class
schwartz2f.fit
inherits from the schwartz2f
class. The
class schwartz2f.fit
adds slots which contain data regarding
the estimation procedure and parameters of the risk-neutral
dynamics. In particular, it adds the market price of convenience yield
risk lambda
and the interest rate.
Objects should only be created by calls to the constructors
schwartz2f
and fit.schwartz2f
.
Slots of class “schwartz2f”:
call
:The function-call of class call
.
s0
:Initial commodity spot-price of class numeric
.
delta0
:Initial value of the convenience yield of
class numeric
.
mu
:Enters the drift of the commodity spot price (under
the objective measure, see Details) of class numeric
.
sigmaS
:Diffusion parameter of the spot price process
of class numeric
.
kappaE
:Speed of mean-reversion of the
convenience-yield process of class numeric
.
alpha
:Mean level of the convenience-yield process of
class numeric
.
sigmaE
:Diffusion parameter of the convenience-yield
process of class numeric
.
rhoSE
:Correlation between the two Brownian motions
which drive the spot price and convenience-yield processes of
class numeric
.
Slots added by class “schwartz2f.fit”:
n.iter
:The number of iterations of class
numeric
.
llh
:The log likelihood value of class
numeric
.
converged
:A logical
stating whether the fit converged or
not.
error.code
:An error code of class numeric
. The
value of optim
's “convergence”. If an unknown
error occurs the value -1 is returned.
error.message
:An error message of class
character
, if any.
fitted.params
:A logical
vector stating which
parameters were fitted.
trace.pars
:Contains the parameter value evolution
during the estimation procedure of class matrix
.
r
:The risk-free interest rate of class numeric
.
alphaT
:The mean-value of the convenience yield
process under the equivalent martingale measure of class
numeric
(see Details).
lambda
:The market price of convenience yield risk of
class numeric
.
meas.sd
:The standard deviation of the measurement
equantion of class numeric
.
deltat
:The time-increment of the transition equation
of class numeric
.
The joint dynamics of the spot-price and the convenience yield are given by the stochastic differential equations
dS = (mu - delta) * S * dt + sigmaS * S * dW1,
d delta = kappa * (alpha - delta) * dt + sigmaE * dW2
dW1 * dW2 = rho dt,
where W1, W2 are Brownian motions under the objective measure.
Under an equivalent martingale measure (the pricing measure) the dynamics is
dS = (r - delta) * S * dt + sigmaS * S * dW1*
d delta = kappa * (alphaT - delta) * dt + sigmaE * dW2*,
where W1*, W2* are Brownian motions with respect to the martingale measure.
alphaT = alpha - lambda / kappa where lambda is the market price of convenience-yield risk.
Class “schwartz2f.fit” extends class “schwart2factor”, directly.
Philipp Erb, David Luethi, Juri Hinz
Stochastic Convenience Yield and the Pricing of Oil Contingent
Claims by Rajna Gibson and Eduardo S. Schwartz
The Journal of
Finance 45, 1990, 959-976
The Stochastic Behavior of Commodity Prices: Implications for
Valuation and Hedging by Eduardo S. Schwartz
Journal of Finance
52, 1997, 923-973
Pricing of Options on Commodity Futures with Stochastic Term
Structures of Convenience Yields and Interest Rates by Kristian
R. Miltersen and Eduardo S. Schwartz
Journal of Financial and
Quantitative Analysis 33, 1998, 33-59
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
schwartz2f
to initialize
schwartz2f
-objects. fit.schwartz2f
to fit the
two-factor model to data and get a schwartz2f.fit
object,
schwartz97-package
for an overview.
1 2 3 4 5 6 7 8 9 10 11 12 | # obj <- schwartz2f() # create an object of class schwartz2f
# obj # print it
# coef(obj) # get coefficients
# unclass(obj) # see the slots
#
# ## create an object of class schwartz2f.fit
# data(futures)
# fit.obj <- fit.schwartz2f(futures$wheat$price, futures$wheat$ttm / 260,
# deltat = 1 / 260, control = list(maxit = 3))
# fit.obj # print it
# coef(fit.obj) # get coefficients
# unclass(fit.obj) # see the slots
|
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