On an ''ultimate risk'' basis that includes the potential loss on derivatives and credit guarantees of different kinds, the figure rises to $US2.51 trillion as of last September, well above the headline figure of $US1.76 trillion in cross-border loans. The sheer scale highlights the systemic dangers if the European Union fails to stabilise the debt crisis.

Euro-zone leaders agreed to boost the lending power of the European Union bailout fund on Friday, but Germany vetoed proposals for a debt buyback scheme or an activist policy of bond purchases.

The BIS, the central bank of central banks, said in its quarterly report that Germany had $US569 billion of exposure to the quartet, France $US380 billion and Britain $US431 billion.

A chunk of British exposure is on behalf of Middle East and Asian clients banking through London. Italy has just $US81 billion at risk and seems uniquely insulated from the crisis.

The geography of risk varies greatly. British-based banks and subsidiaries have $US225 billion at stake in Ireland, and $US152 billion in Spain, but little in Portugal or Greece. France is up to its neck in Greece with $US92 billion; a Benelux-led group has $US180 billion in Spain, and Spain itself has exposure of $US109 billion to Portugal.

The complex web of lending shows how hard it is to contain the problem to one country at a time.

American lenders capitulated in the third quarter, slashing exposure to the four countries by 8.7 per cent. It is likely that US players took advantage of bond purchases by the European Central Bank to sell bonds and cut their losses.

The BIS said global cross-border lending rebounded by $US650 billion in the third quarter to $US31 trillion, but is still far below the $US36 trillion peak in the heady days before the ''great recession''. British-based banks are still leaders with $US5.69 trillion, followed by the US at $US2.92 trillion.

The BIS said Western central banks still enjoyed the benefit of the doubt on pledges to contain inflation, but swap rates have begun to flash warning signals, especially in Britain where two-year inflation swap rates have risen well above the Bank of England's inflation estimates.

The BIS study said the VAT rise accounted for part of the inflation dynamic, but there was also an ''investor wariness of a persistent overshoot''.

While the risk of ''policy mistakes'' by central banks is rising, this is a double-edged threat. US core inflation has fallen to 0.6 per cent. ''In many mature economies, any premature tightening could jeopardise the economic recovery and risk sparking expectations of deflation,'' it said.

Separately, the BIS has recently cracked down on derivative trading. It has demanded higher costs for banks and other participants trading derivatives, equities and bonds.