Calculate the values of \(A(T)\) for a given N-factor model parameters and observations. Primarily purpose is for application within other functions of the NFCP package.
Usage
A_T(parameters, Tt)
Arguments
parameters
A named vector of parameters of an N-factor model. Function NFCP.Parameters is recommended.
Tt
A vector or matrix of the time-to-maturity of observed futures prices
Value
A matrix of identical dimensions to \(T\) providing the values of function \(A(T)\) of a given N-factor model and observations.
Details
Under the assumption that Factor 1 follows a Brownian Motion, \(A(T)\) is given by:
A(T) = ^*T-_i=1^N - 1-e^-_i T_i_i+12(_1^2T +
_i.j 1 _i _j _i,j 1-e^-(_i+_j)T_i+_j)A(T) = mu^* * T - sum_i=1^N (1-e^(-kappa[i] T)lambda[i])/(kappa[i]) + 1/2 (sigma[1]^2 * T)
+ sum_i.j != 1 sigma[i] sigma[j] rho[i,j] (1 - e^(-(kappa[i] + kappa[j]) * T)) / (kappa[i] + kappa[j])
References
Schwartz, E. S., and J. E. Smith, (2000). Short-Term Variations and Long-Term Dynamics in Commodity Prices. Manage. Sci., 46, 893-911.
Cortazar, G., and L. Naranjo, (2006). An N-factor Gaussian model of oil futures prices. Journal of Futures Markets: Futures, Options, and Other Derivative Products, 26(3), 243-268.
# NOT RUN {##Calculate time homogeneous values of A(T) for the##Schwartz and Smith (2000) two-factor model:SS.Oil.A_T <- A_T(SS.Oil$Two.Factor, SS.Oil$Stitched.TTM)
# }