Model Uncertainty in Commodity Markets

Forthcoming: SIAM Journal of Financial Mathematics

40 Pages Posted: 16 May 2015 Last revised: 16 Oct 2015

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Sebastian Jaimungal

University of Toronto - Department of Statistics

Zhen Qin

University of Toronto - Department of Statistics

Date Written: October 15, 2015

Abstract

Agents who acknowledge that their models are incorrectly specified are said to be ambiguity averse, and this affects the prices they are willing to trade at. Models for prices of commodities attempt to capture three stylized features: seasonal trend, moderate deviations (a diffusive factor), and large deviations (a jump factor) both of which mean-revert to the seasonal trend. Here we model ambiguity by allowing the agent to consider a class of models absolutely continuous w.r.t. their reference model, but penalize candidate models that are far from it. We show that the buyer (seller) of a forward contract introduces a negative (positive) drift in the dynamics of the spot price, and enhances downward (upward) jumps so the prices they are willing to trade at are lower (higher) than that of the forward price under P. When ambiguity averse buyers and sellers employ the same reference measure they cannot trade because the seller requires more than what the buyer is willing to pay. Finally, we observe that when ambiguity averse agents price options written on the commodity forward, the effect of ambiguity aversion is strongest when the option is at-the-money, and weaker when it is deep in-the-money or deep out-of-the-money.

Keywords: Ambiguity aversion, Knightian uncertainty, Commodities, Certainty Equivalent, Robust Pricing, Indifference Pricing, Optimal Control

Suggested Citation

Cartea, Álvaro and Jaimungal, Sebastian and Qin, Zhen, Model Uncertainty in Commodity Markets (October 15, 2015). Forthcoming: SIAM Journal of Financial Mathematics, Available at SSRN: https://ssrn.com/abstract=2606679 or http://dx.doi.org/10.2139/ssrn.2606679

Álvaro Cartea (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

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

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

Sebastian Jaimungal

University of Toronto - Department of Statistics ( email )

100 St. George St.
Toronto, Ontario M5S 3G3
Canada

HOME PAGE: http://http:/sebastian.statistics.utoronto.ca

Zhen Qin

University of Toronto - Department of Statistics ( email )

105 St George Street
Toronto, Ontario M5S 3G8
Canada

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