Any futures market provides calendar spreads as well, which represent a price differential between two dates (think: CLK0 is the May contract, CLMO is the June

Any futures market provides calendar spreads as well, which represent a price differential between two dates (think: CLK0 is the May contract, CLMO is the June contract, and CLK0-CLM0 is the difference between the two). CME's systems should trivially handle negative prices because they already have spreads, which are frequently negative.