No, not all central banks in the world are owned by governments or function as statutory bodies.
Lets start with the Bank of England was in fact a private bank owned by slightly more than 1,000 shareholders which included the King and Queen of England and several members of the British royalty. It as also been reported that the Rothschild (London branch) also owned a large portion of the shares.
The Bank of England supposedly was nationalised only in 1946, but the shareholders received Treasury stock on the same dividend yield conditions.
Note that the Bank of England was nationalised in 1946, but the existing holders of Bank of England stock (said to be mostly held by the London branch of the Rothschild family) received £400 of 3% Treasury Stock in exchange for every £100 of their Bank of England stock.
These 3% Treasury Stocks were redeemed by the British government only on 8 May 2015.
In 1946 existing holders of Bank of England stock which at the time paid an annual dividend of 12% received £400 of 3% Treasury Stock in exchange for every £100 of their Bank of England stock, providing them with the same annual income.
3% Treasury Stock was first issued in 1946 by the then Chancellor Hugh Dalton to finance the nationalisation of the Bank of England, over 250 years after a Royal Charter formally creating the Bank was sealed.
The Treasury will redeem the full £35m holding of outstanding debt, which is currently held by around 1000 registered holders, though is not traded regularly. Successive governments have had the option to redeem this stock at par (£100) with 3 months notice since April 1966.
The government is only able to make this announcement because interest rates are lower today, thanks to confidence in the long term economic plan that the government has put in place to cut borrowing and create a resilient economy. Today’s announcement will take advantage of the low yield environment to consolidate the debt portfolio and deliver a long-term benefit to the tax payer.
Same goes to the central bank of the US, which is called the Federal Reserve (or the Fed) is also a privately-owned entity.
The owners of the Federal Reserve Bank of New York (the dominant reserve bank) and the other 11 regional reserve banks are all from a few families – the Rockefellers, the Warburgs, the Schiffs, the Harrimans, the Morgans…and the Rothschilds.
When the Fed was formed, the buyers of its stock were the people who have controlled our political and economic destinies since 1914. They are the Rothschilds, of Europe, Lazard Freres (Eugene Meyer), Kuhn Loeb Company, Warburg Company, Lehman Brothers, Goldman Sachs, the Rockefeller family, and the J.P. Morgan interests.
There have been mergers and a bankruptcy (Lehman brothers, September 15, 2008) but essentially, the Fed stocks are still held by the rich and powerful banking families with the Rothschild (London branch) as the dominant force behind them.