NOT LONG AGO, corporate raider T. Boone Pickens of Mesa Petroleum was asked by MIT economist Lester Thurow what the impact of plunging oil prices would be on his operations. Replied Pickens, "Why, I won't be in trouble unless oil prices drop to $15."

"I assume Mr. Pickens is in trouble," said Thurow as oil prices approached $15 a barrel.

So, potentially, is the entire global financial system. A heavily indebted oil-exporting country -- such as Mexico -- could default on its debts to banks worldwide. That might break the backs of some over-extended American banks, even some of the biggest.

This could cause the world's system for making financial payments -- connected by computers and enmeshed with interlocking and overlapping debts -- to collapse. The shock would be cataclysmic because checks, credit cards and other transfers handled by this vast payments network would be useless.

This prospect is so nightmarish that the Federal Reserve, the nation's central bank, is prepared to use the unlimited amounts of money it has or can create to keep these banks from going under because of imprudent loans.

Ultimately, the defense of the banks and the financial system by the government could make the American taxpayer the lender of last resort to the world.

This sort of scenario used to be no more than the basis for disaster thrillers. Now, however, sober participants in financial markets discuss the possibility seriously. After all, a $40 billion bank, Continental Illinois, failed two years ago. If the Federal Reserve, the FDIC and other agencies had not stepped in, this scenario could have been triggered.

The worry today is not just a single bank, but sweeping losses arising from possible loan defaults by a number of foreign countries and many energy companies that could threaten any of several large banks, whose unanswered failure could produce this catastrophe.

Apart from any urgent concern about a Mexican default, the Federal Reserve is deeply concerned about the safety of the electronic payments network. Those who use it and understand how it works are concerned, too.

The entire payment system is based upon the confidence any bank has, for example, that if it cashes another bank's check, at some point it will get its money back. Today, most of the dollars involved in transactions between banks do not involve checks -- they change hands electronically. Despite this, there is a time gap in such transfers. Yet no one currently worries unduly about it -- resting firm in the belief that all accounts will settle up by the end of the day.

However, if an individual bank failed, this confidence could be destroyed. And if that were to happen, no bank would put money into a transaction unless it were positive that other banks were also keeping up their end of the bargain at exactly the same time -- the way that all parties come together and perform their duties simultaneously at a real estate closing.

But such a procedure is considered, technically, to be so vastly expensive in this complicated globe as to be, for all practical purposes impossible. Therefore, if confidence were lost, the system as we know it would collapse -- with no alternative system in sight.

An example of this kind of weakness is something that the Fed calls a daylight overdraft and is trying, with some success, to eliminate. Just like an individual writing a check shortly before depositing funds to cover it, financial institutions regularly send payments to other institutions via the Fed's electronic transfer system before they have received the incoming credits that they know are on the way.

For years, the Fed operated its system just by adding up all of an institution's credits and debits at the end of each day. So long as they matched, everything was fine.

But then some institutions began to use the system to, in effect, kite checks. At some points during the day, banks were found to be several billion dollars in the hole.

Suppose that in the middle of some day, a large bank failed. It could not honor its obligations and someone would be left unpaid. The Fed would have to cover that possibly multibillion debt immediately or the disaster scenario would be triggered: The banks that were expecting the payment from the failed bank could not, in turn, cover their obligations, the payments system would crash, and so would the current structure of the world's economy.

In this intertwined global financial network, the United States can't let any of the world's major banks collapse, since they all trade with U.S. banks that could be crushed by a major default.

Comptroller of the Currency Todd Conover explicitly told a group of investors after the Continental Illinois collapse that the 11 largest American banks could not be allowed to fail. This meant that the depositers of those institutions did not need to fear losing their money, even if it wasn't covered by deposit insurance.

Conover since has distanced himself from that assurance. Still, given the realities of the payments system, most participants in financial markets understand that the implicit federal guarantee runs much, much farther down the list of institutions than Conover ever suggested.

This interdependence of financial markets explains why everyone is so nervous about the bank failures that might be caused by a Mexican default -- its effects could ripple through the financial system worldwide at the speed of a computer.

Even before the current drop in oil prices, Mexico could not pay what is due this year without large new loans. The Mexican financial situation is so chaotic at this moment that no one even knows where to begin to try to sort it out until oil prices stabilize, according to a senior Reagan administration official.

The uncertainty about Mexico is coupled with heightened concern that some banks, such as the nation's second-largest, the Bank of America, already are under severe pressure from past losses in real estate, agriculture and other areas.

The Bank of America's parent corporation, BankAmerica, earned $1.26 billion last year. But loan losses were even larger, so that the company ended up losing $337 million. Since 1980, the company has written off $4.1 billion in bad loans. It has nearly$7 billion in loans not only to Mexico, but to Venezuela and Brazil.

Domestic energy loans have been a particular problem at many of the other banks now under pressure. A number of large regional banks in Texas and elsewhere got themselves in trouble by lending money to energy companies on the bet that they would be repaid by soaring oil prices. Other loans went to drillers using their rigs as collateral. With the bust in drilling, those rigs now are worth about 10 cents on the dollar.

In the summer of 1984, Continental Illinois was dragged down by enormous loan losses, many in the energy area. Could such a failure happen again? It certainly could. All it really takes is a significant loss of confidence in such a financial institution. And it took billions in FDIC money to transform Continental Illinois into the solvent but much smaller institution it is today.

When Federal Reserve Chairman Paul A. Volcker went before the House Banking Committee last week, Democratic Rep. Henry B. Gonzalez of San Antonio asked bluntly, "How far are you willing to go? You told me once that if necessary you would use all of the United States powers that be to save those banks."

"Well, I don't have all of the United States powers that be at my command . . . ," Volcker replied. "But we certainly conceive of our responsiblilities to use the resources that we have at our command to deal with banking difficulties and crises of the kind that you're contemplating and that I am not."

The following day, facing similar questions in the Senate, the Fed chairman again said that he hoped Mexico might not need the $9 billion worth of new loans that Mexico's government has told American bankers it must have this year.

"I would hope that it isn't that high," Volcker said, "Whatever it is, it will have to be covered or we will have a big problem."

Given enough time and enough earnings against which to write off large loan losses, the threatened banks probably can weather the current storm. From the point of view of the Fed and other agencies of the U.S. government, the least costly way of buying that time may be to spend some money up front -- such as direct aid to Mexico -- rather than face a bank crisis.

But even before oil prices started to fall so swiftly, American and foreign banks were balking at making the additional loans that Treasury Secretary James A. Baker III had suggested should be their share of the $4 billion the Mexicans then were seeking for 1985. The banks, wary of throwing good money after bad, want a federal guarantee for any new loans.

Asked about this possibility, the senior administration official mentioned above said it probably would be a political impossibility. "How can we guarantee loans to Mexico at the same time we are cutting student loan guarantees at home?" he asked.

Such political considerations will complicate any type of assistance, whether it goes to the Mexicans, the energy companies or the banks.

One way or another, it will have to be forthcoming, because the alternative, a collapse of the financial payments system, would be intolerable.