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<\/figure>\n\n\n\nFig. 1: Time series of basis (futures price \u2014 spot price) for soybeans (left) and corn (right) futures. During 2004\u20132009, the expiring futures price tends to be significantly higher than the spot price. Source: Tim Leung https:\/\/doi.org\/10.1016\/j.jcomm.2017.04.001<\/a>. See Reference section for details.<\/em><\/p>\n\n\n\n There\u2019s also a clear\u202fseasonality<\/strong>\u202fin the basis. The average bases for corn, soybeans, and wheat is highest during the harvest months (August-October) as storage rates are high due to grain silo capacity constraint. For instance, the average basis for soybeans exceeds 12% in September. From February to June, the basis tends to be smaller since the storage costs are lower due to empty grain silos before the next harvest begins. <\/p>\n\n\n\n Seasonality of the average basis for corn, soybeans, and wheat during 2004\u2013 2010. <\/em> The report by Irwin et al. (2009)<\/a>\u202ffirst coined the term \u201cnon-convergence\u201d for this phenomenon of observed positive premium, which recurred persistently from 2004 onwards. According to their study, \u201cperformance has been consistently weakest in wheat, with futures prices at times exceeding delivery location cash prices by $1.00\/bu, a level of disconnect between cash and futures not previously experienced in grain markets.\u201d <\/p>\n\n\n\n Long-Side Options<\/strong> <\/p>\n\n\n\n However, a small difference between expiring futures and cash prices does not necessarily imply a market failure. Before expiration, futures and cash prices may differ due to the convenience yield, storage costs, or financing costs. <\/p>\n\n\n\n Upon expiration, if cash prices are lower\/higher than futures prices, then arbitrageurs may profit from trading simultaneously in the spot and futures markets. If sufficient numbers of arbitrageurs engage in these trades, they will drive cash and futures prices to convergence at expiration. <\/p>\n\n\n\n In fact, the futures expiration date and delivery date may also differ. After the last trade date, the exchange contacts the longest outstanding long who is notified of his obligation to undertake delivery. Before the month\u2019s end, the delivery instrument is then exchanged at the settlement price between long and short parties. Therefore, since the delivery process does not occur immediately after the last trade date, cash and futures prices might still differ. <\/p>\n\n\n\n Since the short party may choose the location and time to deliver, one may argue that futures price should be biased below the spot price on the last trade date. However, this would yield the opposite of the empirical observations in the grain markets. In fact, the\u202fpositive<\/em>\u202fbasis in the CBOT grain markets between 2004\u20132009 were too large to have been caused by the small inefficiencies of the delivery process. In order to explain the positive premium, one must turn to embedded long-side options in the futures. <\/p>\n\n\n\n Long-side options<\/strong>\u202fin futures markets depend totally on the idiosyncrasies of each commodity\u2019s exchange traded structure. The appropriate model for a commodity varies highly depending on storability, instantaneous utility, and alternatives. <\/p>\n\n\n\n At expiration, a CBOT agricultural futures contract does not deliver the physical grains but an artificial instrument called the\u202fshipping certificate<\/strong>\u202fthat entitles its holder to demand loading of the grains from a warehouse at any time. Before exercising the option to load, the holder must pay a fixed storage fee to the storage company, as stipulated in the certificate. <\/p>\n\n\n\n Since the storage capacity of grain elevators is limited and expensive, the number of grain elevators is fixed to a minimum necessary to efficiently carry out transfers of grain from one transport system to another. Thus, like a fractional-reserve banking system, shipping certificates alleviate the congestion of grain elevators by only keeping enough grain on hand to satisfy instant withdrawal demand. <\/p>\n\n\n\n Stochastic Storage Cost Model for Grains Futures<\/strong> <\/p>\n\n\n\n In Guo and Leung (2017), we present a storage differential hypothesis: when the certificate storage rate is sufficiently low, investors will pay a premium for the certificate over the spot grain in order to save on storage cost over time, resulting in non-convergence of futures and spot prices. <\/p>\n\n\n\n When the storage cost of the certificate is set lower than the true storage cost paid by the regular firm, the regular firm will cease to issue the unprofitable shipping certificates. Since shipping certificates can only be issued by a set number of regular firms with limited inventories, the market cannot issue certificates with lower fixed storage rates to keep the market flowing. Instead, since the supply of certificates remains fixed, the value of existing shipping certificates will be bid up in the secondary market, resulting in a premium over the spot price. <\/p>\n\n\n\n On the other hand, during periods where the certificate storage rate is set much higher than the market storage rate, the certificate should not command any premium over the spot because agents would exercise and store at the lower market rate. Therefore, large quantities of certificates remaining unredeemed under the storage differential hypothesis becomes a strong indicator of non-convergence. In fact, under mounting evidence that storage differentials were responsible for non-convergence, the CBOT raised the certificate storage rate for wheat, after which non-convergence decreased significantly. This observation is consistent with our findings in this paper. <\/p>\n\n\n\n We propose two new models that incorporate the stochasticity of the market storage rate and capture the storage option of the shipping certificate by solving two optimal timing problems, namely, to exercise the shipping certificate and subsequently liquidate the physical grain. <\/p>\n\n\n\n By examining the divergence between expiring futures prices and corresponding spot prices, we derive the\u202ftiming option<\/strong>\u202fgenerated by the differential between the\u202fmarket storage rate<\/strong>\u202fand the constant storage rate stipulated in the shipping certificate, which explains the non-convergence phenomenon in agricultural commodity markets. <\/p>\n\n\n\n The core mathematical problem within our\u202fstochastic storage cost models<\/strong>\u202fis an\u202foptimal double stopping<\/em>\u202fproblem. To this end, we adapt to our problem the results developed by\u202fLeung et al. (2015)<\/a>\u202fthat study the optimal entry and exit timing strategies when the underlying is a mean-reverting process. <\/p>\n\n\n\n Among our results, we provide\u202fexplicit prices\u202f<\/strong>for\u202fthe shipping certificate<\/strong>,\u202ffutures prices<\/strong>, and the\u202fbasis<\/strong>\u202fsize under a two continuous-time no-arbitrage pricing models with stochastic storage rates. We also fit our model prices to market data and extract the numerical value of the embedded timing option. <\/p>\n\n\n\n Source: Tim Leung https:\/\/doi.org\/10.1016\/j.jcomm.2017.04.001<\/a>. See Reference section for details.<\/em><\/p>\n\n\n\n Source: Tim Leung https:\/\/doi.org\/10.1016\/j.jcomm.2017.04.001<\/a>. See Reference section for details.<\/em><\/p>\n\n\n\n Source: Tim Leung https:\/\/doi.org\/10.1016\/j.jcomm.2017.04.001<\/a>. See Reference section for details.<\/em><\/p>\n\n\n\n Calibrated futures curves with and without the shipping certificate. Clearly shipping certificate carries a positive value that\u2019s embedded in the futures contract. <\/p>\n\n\n\n References<\/strong><\/p>\n\n\n\n K. Guo and T. Leung (2017). Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options, Journal of Commodity Markets, Vol 6, June 2017, Pages 32\u201349 [pdf<\/a>;link<\/a>]<\/p>\n\n\n\n T. Leung T. and X. Li (2015), Optimal Mean Reversion Trading with Transaction Costs & Stop-Loss Exit, International Journal of Theoretical & Applied Finance, vol 18, issue 3, p.1550020. [pdf<\/a>;link<\/a>]<\/p>\n\n\n\n Irwin, S. H., Garcia, P., Good, D., and Kunda, E. (2009). Poor convergence performance of CBOT corn, soybean and wheat futures contracts: Causes and solutions. Marketing and Outlook Research Report<\/em><\/p>\n","protected":false},"excerpt":{"rendered":" Join Tim Leung for a look at Non-Convergence Between Futures and Spot Prices in the Grains Market. “The core mathematical problem within our\u202fstochastic storage cost models\u202fis an\u202foptimal double stopping\u202fproblem. To this end, we adapt to our problem the results developed by\u202fLeung et al. (2015)\u202fthat study the optimal entry and exit timing strategies when the underlying is a mean-reverting process.” <\/p>\n","protected":false},"author":189,"featured_media":84307,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[339,338,341,352,344],"tags":[4923,4922,1226,169,9573,9571,494,5926,9572,4271],"contributors-categories":[13668],"class_list":["post-84209","post","type-post","status-publish","format-standard","has-post-thumbnail","category-data-science","category-ibkr-quant-news","category-quant-development","category-quant-north-america","category-quant-regions","tag-computational-finance","tag-econometrics","tag-financial-engineering","tag-futures","tag-grains-market","tag-non-convergence","tag-quant","tag-quantamental","tag-spot-prices","tag-statistical-arbitrage","contributors-categories-computational-finance-risk-management-university-of-washington"],"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"\n![\"Image](\"\/campus\/wp-content\/uploads\/sites\/2\/2021\/04\/image-70-1100x741.png\")
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Source: Tim Leung https:\/\/doi.org\/10.1016\/j.jcomm.2017.04.001<\/a>. See Reference section for details.<\/em><\/p>\n\n\n\n![\"Image](\"\/campus\/wp-content\/uploads\/sites\/2\/2021\/04\/image-71.png\")
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