On Monday, the crisis seemed to be abating. But now we know better ...

They may have saved the banks; but can they save the world from recession? The markets have clearly had some difficulty answering the second question, even if they are sometimes comparatively calm on the first point, having seen the colour of taxpayers' money. "Roller coaster ride" may be bit of a stock market report's cliché, but it fitted the profile of last week's share indices perfectly.

In quieter times, yesterday's gyrations on the stock markets would have made dramatic news. By recent standards, they were blessedly dull. In the US, shares opened 200 points lower, with fears of recession fuelled by yet more dismal news from the property market. The Dow Jones recovered later, but it was a startling stumble. In Europe, things seemed, relatively, brighter, though things bounced around a lot there as well. The FTSE 100 ended up 4.6 per cent; Germany's Dax index rose 4 per cent and France's Cac 40 was 3.8 per cent more valuable. In Tokyo, the Nikkei ended up 2.8 per cent.

It marked the end of yet another trip on the Big Dipper, one that certainly unsettled quite a few tummies.

The ups were invigorating: pushed along by optimism that, at last, the governments of the biggest economies had got their act together. The beginning of the week saw huge share price increases. The FTSE was up 8 per cent; the Dow soared by 11 per cent, and in Paris the bourse was also up 11 per cent – its best day in history. Why? Because investors and traders could at last dare to believe that, this time, the worst really was over for the banks. Lending money to them hadn't worked despite a year of trying. Now they were being given the cash they needed – a vast subsidy from taxpayers to bankers and householders who made some big mistakes during the bubble. No wonder the City liked it.

On Monday, Gordon Brown and Alistair Darling announced which banks were to be beneficiaries of the taxpayers' £37bn share-buying spree, part of a £500bn rescue plan; the German and French governments announced €1trn of aid to their banks. The US Treasury let it be known that $250bn of the $700bn "Paulson Plan" would be spent on buying shares in America's leading financial institutions.

Weeks of ineffectual posturing were put behind them. George Bush alone called for calm on 20 separate occasions during the past few weeks; he did again yesterday. His words never penetrated the din of panic. This is, as Mr Brown realised, a time for actions not words. At the IMF conference and G7 summits in Washington over the weekend, and at an emergency European summit, the world's leaders agreed on what to do and – more importantly – also agreed to get on with doing it. The usual IMF Communiqué had been replaced by a "Plan of Action". Diplomacy got its chequebook out.

Yet the tensions in the markets soon returned. Pulled up by optimism abut the banks, soon enough the black dog of depression began to haunt them. It was almost as if the world had temporarily forgotten about the real economy. Yet later on Tuesday, and with breathtaking force on Wednesday and Thursday, the world woke up and remembered its other nightmare – a full-blown global recession. The closing stages of Tuesday's trading saw ominous signs of the rally flagging. Wall Street lost its gains, though London hung on to some progress. Worse was to follow.

The news that broke on Wednesday was bad. Americans, the world's "consumers of last resort", were losing their appetite for shopping. US retail sales fell to their lowest in more than three years. It was perfectly obvious who that was hurting. Last year, the US managed to run up a deficit of $256bn with China, her biggest trading partner. If Americans stop buying Chinese DVD players, dog food, toys and toothpaste, then China will begin to stumble. Markets across Asia reacted badly, and the fear of global recession spread across every time zone. The mining stocks, bloated on the back of the appetite for coal, copper, zinc and the other raw materials of the Chinese industrial revolution, collapsed. The price of oil slumped to below $70 a barrel, half the $147 highs of July.

With scores of stock market records shattered over recent weeks, the Dow managed to break one of the most formidable; it saw its worst single day since the crash of 1987. The FTSE dropped by 7 per cent, pushing it well below the 4,000-point barrier; its recent peak in July last year was 6,754. No wonder; UK unemployment reached a 17-year high, with another 164,000 Britons losing their jobs.

If anything, things seemed even grimmer on Thursday. By now, our roller coaster had entered its downward slopes. On top of Wednesday's losses were piled still more; the FTSE down another 5 per cent; the Nikkei, reflecting corporate Japan's symbiotic relationship with China, down by 11 per cent, its worst day since 1987. And, just as the world was beginning to dare to feel hopeful about the banks, the Swiss announced a £38bn package of aid for UBS. Given that UBS looks after $2trn in pension and other funds, renewed worries about the financial sector were inevitable, as were the consequences. More than $2trn has been wiped from the retirement funds of Americans alone in the past year.

As the world staggers giddily from its less-than-fun ride, a couple of things seem clear. First that the new worry is recession, and the hope that China could simply pull the rest of the world through a slump has been shown to be vain. Second that this level of volatility is here to stay. For the analysts the proof lies in an esoteric corner – something called the "Vix" index, run by the Chicago Board of Trade. It's a measure of how bouncy share markets are, and the index shows that they have probably never been as volatile as they are now. There are huge uncertainties abroad. Will more banks crash? Will more countries follow Iceland into bust? How bad will the recession be? No one knows the answer, and the markets generally react badly to such doubts. Fasten your seat belts.