cov_func: N-factor model covariance:

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

N-factor model covariance:

Description

\loadmathjax

Calculate the covariance matrix of state variables for a given N-factor model parameters and discrete time step.

Usage

cov_func(parameters, dt)

Arguments

parameters	a named vector of parameters of an N-factor model. Function NFCP_parameters is recommended.
dt	a discrete time step

Details

The primary purpose of the model_covariance function is to be called within other functions of the NFCP package. The covariance of an N-factor model is given by:

\mjdeqn

cov_1,1(x_1,t,x_1,t) = \sigma_1^2tcov[1,1](x[1,t],x[1,t]) = sigma[1]^2 * t \mjdeqncov_i,j(x_i,t,x_j,t) = \sigma_i\sigma_j\rho_i,j\frac1-e^-(\kappa_i+\kappa_j)t\kappa_i+\kappa_jcov[i,j](x[i,t],x[j,t]) = sigma[i] sigma[j] rho[i,j] (1-e^(-(kappa[i]+kappa[j])t ) / (kappa[i] + kappa[j])

Value

A matrix object with dimensions \mjeqnN \times NN X N, where N is the number of factors of the specified N-factor model.

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 the covariance matrix of a two-factor model over one discrete (weekly) time step:
SS_oil.covariance <- cov_func(SS_oil$two_factor, SS_oil$dt)

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