Doesn't look like there's anything exchange traded according to Bloomberg + the Baltic Excghange's web site gives this when attempting to look at prices . . .
"A summary of the Baltic Dry Index (BDI), Baltic Capesize Index (BCI), Baltic Panamax Index (BPI), Baltic Supramax Index (BSI), Baltic Handysize Index (BHSI) and Baltic International Tanker Routes (BITR). Access to this data is by subscription only." ie no-one could accuse it of being a transparent index!
So I'm guessing it's effectively untradable.