Duh . . .
Yes, it is true that there were no "exchange-traded" options that expired on December 31st. However, many investment banks and their equity-derivative desks have the ability to create and customize collars on individual equities as well as equity indexes such as the S&P 100 and 500.
As a result, the surge in volume in puts that were traded in the last 2 days of the year are indicative of the types of strategies listed above being executed. There are also quarterly expirations as well, while June 30th sees a fairly large share of customized options, collars, and hedges going off.
Ask anyone that works on an equity-derivatives desk.
They will tell you that collars and other types of hedges are created and unwound all the time, with no relation to exchange traded expirations.
ie.) Ever wonder why a market will SURGE past an important round figure in the S&P or Dow, or BREAKDOWN below a significant "psychological" level as well?
Answer: Collars