NFCP: A_T – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

A_T

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

Under the assumption that Factor 1 follows a Brownian Motion, A(T) is given by: \[A(T) = \mu^*T-\sum_{i=1}^N - \frac{1-e^{-\kappa_i T}\lambda_i}{\kappa_i}+\frac{1}{2}(\sigma_1^2T + \sum_{i.j\neq 1} \sigma_i \sigma_j \rho_{i,j} \frac{1-e^{-(\kappa_i+\kappa_j)T}}{\kappa_i+\kappa_j})\]

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

N-Factor Commodity Pricing Through Term Structure Estimation

v1.0.1

GPL-3

Authors

Thomas Aspinall [aut, cre] (<https://orcid.org/0000-0002-6968-1989>), Adrian Gepp [aut] (<https://orcid.org/0000-0003-1666-5501>), Geoff Harris [aut] (<https://orcid.org/0000-0003-4284-8619>), Simone Kelly [aut] (<https://orcid.org/0000-0002-6528-8557>), Colette Southam [aut] (<https://orcid.org/0000-0001-7263-2347>), Bruce Vanstone [aut] (<https://orcid.org/0000-0002-3977-2468>)

Initial release

A_T