schwartz97-package:
Two-factor Commodity Model

Description

This package contains an implementation of the Schwartz two-factor commodity model, that is, the joint dynamics of the spot price and the spot convenience yield according to Schwartz (1997). The parameter estimation function constitutes the core of this package. Once the parameters are estimated, futures and European call and put options can be priced, term structures can be calculated and the usual distribution operations d/p/q/r can be carried out on the state variables as well as on futures prices. The package is accompanied by a variety of utility functions, futures data of ten commodities, and two vignettes describing technical details and usage of the package.

Arguments

Details

Package:

schwartz97

Type:

Package

Version:

0.0.4

Date:

2011-12-18

License:

GPL (GNU Public License), Version 2 or later

Initialization:

schwartz2f

Initialize a Schwartz two-factor object.

Density, distribution function, quantile function, random number generation, and trajectories of the state variables:

dstate

Density of the spot and the convenience yield.

pstate

Distribution of the spot and the convenience yield.

qstate

Quantile of the spot and the convenience yield.

rstate

Random number generation of the spot and the convenience yield.

simstate

Trajectory of the spot and the convenience yield.

Density, distribution function, quantile function, and random number generation of the futures price:

dfutures

Density of the futures price.

pfutures

Distribution of the futures price.

qfutures

Quantile of the futures price.

rfutures

Random number generation of the futures price.

Parameter estimation:

fit.schwartz2f

Estimate parameters of the two-factor model.

fitted

Extract the model's fitted values.

resid

Extract model residuals.

Pricing:

pricefutures

Compute arbitrage-free futures prices.

priceoption

Compute arbitrage-free European option prices.

Utilities:

coef

Extract model coefficients of schwartz2f-objects.

mean

Extract the mean of schwartz2f-objects.

vcov

Extract the covariance matrix of schwartz2f-objects.

filter.schwartz2f

Filter futures prices to get the spot price and convenience yield.

plot

Plot schwartz2f.fit-objects.

plot

Plot trajectories of schwartz2f-objects.

futures

Use data(futures) to get data of 10 commodities.

Package vignette:

The R package schwartz97 contains two vignettes:

The vignette Technical Document gives the necessary relations and tools to fully understand the internals of the package.

The vignette User Guide discusses implementation details and gives numerous examples and intuitive explanations.

References

Stochastic Convenience Yield and the Pricing of Oil Contingent Claims by Rajna Gibson and Eduardo S. Schwartz The Journal of Finance 45, 1990, 959-976

The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging by Eduardo S. Schwartz Journal of Finance 52, 1997, 923-973

Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates by Kristian R. Miltersen and Eduardo S. Schwartz Journal of Financial and Quantitative Analysis 33, 1998, 33-59

Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot by Jimmy E. Hilliard and Jorge Reis Journal of Financial and Quantitative Analysis 33, 1998, 61-86