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1. Introduction
The Chicago Board of Trade[1] (CBOT) offers trading of calendar spread options on futures in wheat, corn, soybean, soybean oil, soybean meal and live cattle, and the New York Mercantile Exchange offers trading of calendar spread options on cotton and crude oil. Calendar spread options were created to provide a risk management tool that was unavailable with any combination of previous contracts. With calendar spread options markets, storage facilities can purchase a calendar spread call option to hedge the risk of futures spread narrowing or inverting. This can be especially helpful when the maturity of the cash position does not exactly match any of the futures options maturities. Similarly, grain elevators can use calendar spread options to partially offset the risk of offering hedge-to-arrive contracts.
Calendar spreads are the difference between futures prices of the same commodity with different delivery dates. The CBOT definition of calendar spread is the nearby futures minus distant futures (this may seem backward, but that is what is done). Options on calendar spreads cannot be replicated by combining two futures options with different maturity dates. The reason is that calendar spread options are affected only by volatility and value of the price relationship while any strategy to replicate the spread using futures options is also sensitive to the value of the underlying commodity (Chicago Mercantile Exchange Group, 2015a).
Despite such benefits, the volume of calendar spread options traded has been low. Table I presents the volume of CBOT futures, options and calendar spread options in 2014 and the open interest for a date in 2017. In 2014, the volume across all of these agricultural calendar spread option markets was 0.2 percent that of futures contracts, while regular options had 26 percent of the volume that futures did. As options are more often held to maturity, in 2017 calendar spread options had 1.2 percent of the open interest of futures while regular options had 74 percent of the open interest of futures. First, these numbers indicate that calendar spread options are being traded. But, the relatively small volume may be partly due to the lack of an accurate model to price calendar spread options. A more precise pricing formula would allow option traders to lower bid-ask spreads as has...