futures_price_simulate {NFCP}

Simulate futures prices of an N-factor model through Monte Carlo simulation

Description

Simulate Futures price data with dynamics that follow the parameters of an N-factor model through Monte Carlo simulation.

Usage

futures_price_simulate(
  x_0,
  parameters,
  dt,
  N_obs,
  futures_TTM,
  ME_TTM = NULL,
  verbose = TRUE
)

Arguments

x_0

vector. Initial values of the state variables, where the length must correspond to the number of factors specified in the parameters.

parameters

vector. A named vector of parameter values of a specified N-factor model. Function NFCP_parameters is recommended.

dt

numeric. Discrete time step, in years, of the Monte Carlo simulation.

N_obs

numeric. Number of discrete observations to simulate.

futures_TTM

vector or matrix. The time-to-maturity of observed futures contracts, in years, at a given observation date. This time-to-maturity can either be constant (ie. class 'vector') or variable (ie. class 'matrix') across observations. The number of rows of object 'futures_TTM' must be either 1 or equal to argument 'N_obs'. NA values are allowed.

ME_TTM

vector. the time-to-maturity groupings to consider for observed futures prices. The length of ME_TTM must be equal to the number of 'ME' parameters specified in object 'parameter_names'. The maximum of 'ME_TTM' must be greater than the maximum value of 'futures_TTM'. When the number of 'ME' parameter values is equal to one or the number of columns of object 'log_futures', this argument is ignored.

verbose

logical. Should simulated state variables be output?

Details

The futures_price_simulate function simulates futures price data using the Kalman filter algorithm, drawing from a normal distribution for the shocks in the transition and measurement equations at each discrete time step. At each discrete time point, an observation of the state vector is generated through the transition equation, drawing from a normal distribution with a covariance equal to \(Q_t\). Following this, simulated futures prices are generated through the measurement equation, drawing from a normal distribution with covariance matrix equal to \(H\).

Input futures_TTM can be either a matrix specifying the constant time to maturity of futures contracts to simulate, or it can be a matrix where nrow(futures_TTM) == N_obs for the time-varying time to maturity of the futures contracts to simulate. This allows for the simulation of both aggregate stitched data and individual futures contracts.

Value

futures_price_simulate returns a list with three objects when verbose = T and a matrix of simulated futures prices when verbose = F. The list objects returned are:

#'

state_vector	A matrix of Simulated state variables at each discrete time point. The columns represent each factor of the N-factor model and the rows represent the simulated values at each discrete simulated time point.
futures_prices	A matrix of Simulated futures prices, with each column representing a simulated futures contract.
spot_prices	A vector of simulated spot prices

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

# Example 1 - Simulate Crude Oil with constant time-to-maturity:

simulated_futures <- futures_price_simulate(x_0 = c(log(SS_oil$spot[1,1]), 0),
                                           parameters = SS_oil$two_factor,
                                           dt = SS_oil$dt,
                                           N_obs = nrow(SS_oil$stitched_futures),
                                           futures_TTM = SS_oil$stitched_TTM)

##Simulate Crude Oil Contracts with a rolling-window of measurement error:

simulated_futures_prices <- futures_price_simulate(x_0 = c(log(SS_oil$spot[1,1]), 0),
                                                  parameters = SS_oil$two_factor,
                                                  dt = SS_oil$dt,
                                                  N_obs = nrow(SS_oil$contracts),
                                                  futures_TTM = SS_oil$contract_maturities,
                                                  ME_TTM = c(1/4, 1/2, 1, 2, 5))