Calibration and Filtering for Multi Factor Commodity Models with Seasonality: Incorporating Panel Data from Futures Contracts

Methodology and Computing in Applied Probability 15(4), pp. 841-874, December 2013, DOI 10.1007/s11009-012-9286-7

Posted: 29 Nov 2014

See all articles by Gareth Peters

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Mark Briers

QinetiQ Ltd

Pavel V. Shevchenko

Macquarie University; Macquarie University, Macquarie Business School

Arnaud Doucet

University of Cambridge - Department of Engineering

Date Written: July 11, 2011

Abstract

We construct a general multi-factor model for estimation and calibration of commodity spot prices and futures valuation. This extends the multi-factor long-short model in Schwartz and Smith (2000) and Yan (2002) in two important aspects: firstly we allow for both the long and short term dynamic factors to be mean reverting incorporating stochastic volatility factors and secondly we develop an additive structural seasonality model. In developing this non-linear continuous time stochastic model we maintain desirable model properties such as being arbitrage free and exponentially affine, thereby allowing us to derive closed form futures prices. In addition the models provide an improved capability to capture dynamics of the futures curve calibration in different commodities market conditions such as backwardation and contango. A Milstein scheme is used to provide an accurate discretized representation of the s.d.e.model. This results in a challenging non-linear non-Gaussian state-space model. To carry out inference, we develop an adaptive particle Markov chain Monte Carlo method. This methodology allows us to jointly calibrate and filter the latent processes for the long-short and volatility dynamics. This methodology is general and can be applied to the estimation and calibration of many of the other multi-factor stochastic commodity models proposed in the literature. We demonstrate the performance of our model and algorithm on both synthetic data and real data for futures contracts on crude oil.

Keywords: Multi-factor, Commodity, spot price, Stochastic volatility, Milstein, Adaptive Markov chain Monte Carlo, Particle filter, Rao-Blackwellization

JEL Classification: C1

Suggested Citation

Peters, Gareth and Briers, Mark and Shevchenko, Pavel V. and Doucet, Arnaud, Calibration and Filtering for Multi Factor Commodity Models with Seasonality: Incorporating Panel Data from Futures Contracts (July 11, 2011). Methodology and Computing in Applied Probability 15(4), pp. 841-874, December 2013, DOI 10.1007/s11009-012-9286-7, Available at SSRN: https://ssrn.com/abstract=2531821

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Mark Briers

QinetiQ Ltd ( email )

United Kingdom

Pavel V. Shevchenko

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

HOME PAGE: http://www.businessandeconomics.mq.edu.au/contact_the_faculty/all_fbe_staff/pavel_shevchenko

Macquarie University, Macquarie Business School ( email )

New South Wales 2109
Australia

Arnaud Doucet

University of Cambridge - Department of Engineering ( email )

Cambridge
United Kingdom

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