The CME just released an announcement that is intended to make clear that Case Shiller options have European-style (at expiration) and not American-style (continuous) rules. http://www.cmegroup.com/notices/ser/2016/07/SER-7688/SER-7713.pdf
Since the futures don’t have coupon payments or dividends, and since options always have some time value, I’ve long analyzed these options as European. I could see where someone might back into a position where they sell futures against a put they’ve bought that has gone deep in the money (to lock in gains). I’d be open to orchestrating an unwind, if needed.
If you have questions on options, or any other aspect of hedging home prices, please feel free to contact me here (firstname.lastname@example.org).