As Califgal said, Staroptions expire at the end of the calendar year. With an every year timeshare you can borrow Starpoints from the next year, but not with an EOY week.
The only way to use an EOY TS during the off year is to deposit it with an outside exchange company, and make an exchange during the off year.
StarPOINTS however, do carry over from one year to another.
For more info. about how Starwood works, see the Starwood FAQ at the top of the board.