Asymptotic Exponential Arbitrage in a Liu-Tang 3-Factor Model of Commodity Futures

Abstract

From a 3-factor model of storable commodities discussed by Liu and Tang (2010), we consider a cash market model such as futures exchange with a single futures contract on one such commodities and a money market account. After verifying that this model is arbitrage-free and incomplete in any finite time horizon or delivery date, we show that there still exists a possibility to generate exponentially growth risk-less profit in long term; a form of asymptotic arbitrage conjectured by Föllmer and Schachermayer (2008) and first solved by Mbele Bidima and Rásonyi (2012) in financial security models. And we find that works in this paper generalize our recent works in Tadesse Welemical et al. (2019) on Schwartz’s one-factor model of commodity futures.