For the past several years, JP Morgan held the most silver on a public exchange in the world.  While the LBMA may hold (or did hold) more silver, their stockpiles are not made public.

Regardless, JP Morgan held the most silver at nearly 74 million oz (Moz) in its warehouse, up until recently.  Over the past two months, JP Morgan's silver inventories have fallen nearly 7 Moz to 67.1 Moz today:

As I mentioned in my previous article, Why Are The Chinese Stockpiling Silver? Big Move Coming?, JP Morgan increased their silver inventories from 4 Moz in April 2011 to 69.4 Moz April 19, 2016.  However, the Shanghai Futures Exchange silver inventories surged from 7.5 Moz in August 2015 to 54.7 Moz on April 19, 2016: