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• Greeks dive for bank under the bed
The Athens Stock Exchange will also be closed today.
The moves were introduced to staunch the flow of money out of Greek banks and spur the country's creditors to offer concessions before a bailout programme expires at midnight on Wednesday (NZ time).
The accelerating crisis has thrown into question Greece's financial future and continued membership in the 19-nation shared euro currency.
Craigs Investment Partners head of private wealth research, Mark Lister, said Europe was in better economic shape, economically, to deal with the fallout from Greece than it had been in the past.
"But the risks are still plentiful," he said. "If it gets worse we will feel the heat, for sure, but in a more modest way than European sharemarkets."
Lister said the market volatility was likely to continue for the rest of this week and into the next.
"It's looking pretty bleak."
After Greece's current bailout expires, the €7.2 billion euros remaining in it will no longer be available.
Without those funds, Greece is unlikely to be able to pay a €1.6 billion-euro International Monetary Fund debt repayment.
In the referendum set for next Sunday, the Greek Government is urging its citizens to vote against its creditors' proposals, arguing that they are humiliating and that they would prolong the country's financial woes.
"There's a bit of uncertainty as to how this all going to play out and the markets obviously hate that uncertainty," said Grant Williamson, of sharebrokers Hamilton Hindin Greene. "Until that uncertainty is removed then markets are likely to be trending downwards."
Australia - nearly $40b wiped out
Australia's share market has suffered one of its biggest falls in years, with nearly $40 billion wiped out as Greece inches towards a default on its debt and a potentially catastrophic exit from the euro zone.
Australia's market was caught up in a global sell off stemming from the collapse of debt negotiations between Greece and its European Union and International Monetary Fund creditors.
Greece needs to repay 1.6 billion euros of loans to the IMF by Tuesday to avoid defaulting on its debt.
Investors had widely expected the two sides to do what they have done many times before and strike an 11th-hour deal.
But Greek Prime Minister Alexis Tsipras derailed the talks and stunned Europe by announcing a referendum for July 5 on the creditors' proposed reform package that would see the country cut pensions and raise taxes to pay its debts.
Mr Tsipras's Syriza party is urging citizens to vote against the reform package in a move that could precipitate Greece's departure from the euro zone.
News of the collapse of talks sent a shudder through global markets, with Japan's Nikkei and Hong Kong's Hang Seng both down more than two per cent.
Australia's market index, the S&P/ASX 200, plunged 2.2 per cent to 5,422.5, its lowest level since January.
The pain is set to continue once European and US markets open, with Germany's DAX 30 expected to open four per cent lower.
There were few places to hide on the Australian market, with the major banks, miners, retailers, healthcare providers and telcos all sharply lower.
Only a small number of companies managed to score gains, most of which were gold miners as traders looked for safe haven assets to avoid the carnage.
A Greek exit from the euro zone could have an impact on Australian Greeks.
If it leaves, Greece will need a new currency, which UNSW economist Tim Harcourt says will be worth somewhere between 50 per cent and 60 per cent of the euro.
That would be bad news for savers, including Greek Australians with bank accounts in their homeland.
"Anyone holding euros in cash would immediately be much richer.
But those Greek Australians with euros in an Athens bank account would be badly hurt," he said.
IG markets strategist Evan Lucas said while the Australian market had little direct exposure to Greece, traders were concerned about what a Greek exit from the euro zone, or Grexit, would mean for other debt-laden EU countries including Italy and Spain.
"There is not much you can point to in terms of how this will end and markets hate uncertainty."
Greece is in the midst of arguably the worst economic crisis experienced by a developed country in modern times.
Its economy has shrunk by about a quarter in a depression that has so far lasted more than six years, while its unemployment rate is hovering above 25 per cent.
Greece has closed its banks for a week to prevent people withdrawing all of their savings and is limiting ATM withdrawals to help head off the potential for a collapse of the country's financial system.
- AAP