A_T: Calculate A(T)

In NFCP: N-Factor Commodity Pricing Through Term Structure Estimation

Calculate A(T)

Description

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

Details

\loadmathjax

Under the assumption that Factor 1 follows a Brownian Motion, A(T) is given by: \mjdeqnA(T) = \mu^*T-\sum_i=1^N - \frac1-e^-\kappa_i T\lambda_i\kappa_i+\frac12(\sigma_1^2T + \sum_i.j\neq 1 \sigma_i \sigma_j \rho_i,j \frac1-e^-(\kappa_i+\kappa_j)T\kappa_i+\kappa_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])

Value

A matrix of identical dimensions to T providing the values of function A(T) of a given N-factor model and observations.

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.

Examples

##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)

NFCP documentation built on March 18, 2022, 5:06 p.m.