The New York Stock Exchange announced today that it has formally asked government permission to set up a financial futures trading market.

The nation's largest securities exchange said it hopes to begin trading in seven different financial contracts - Treasury bills, Treasury bonds and five major currencies - by early next year.

Futures contracts are agreements to buy or sell a specified quantity of some commodity at a specified date and price. Usually futures trading has been carried out in agricultural commodities such as wheat or soybeans.

But in recent years trading of futures contracts in Treasury securities, foreign currencies and, most recently, mortgage securities has been growing rapidly.

So far, most of the financial futures trading has been concentrated in Chicago - at the Board of Trade and Mercantile Exchange - where most of the nation's trading in commodity futures is located.

But the American Stock Exchange has been trading Government National Mortgage Association futures for some months.

Earlier this week, the Commodities Futures Trading Commission, which must approve the NYSE plan, approved four new contracts for trading in government securities, one each for the two Chicago exchanges, another for the Amex operation and a fourth for New York's Commodities Exchange Inc. (Comex), which specializes in futures trading in metals.

The NYSE, when it became interested in setting up futures trading last year, held merger and joint venture talks with both the Amex and the Comex, but then last March decided to go it alone.

If the CFTC approves the Big Board's plan - the application took up 12 volumes and 1,800 pages - the financial strength of the exchange and its location in New York City, where most of the nation's foreign exchange trading takes place, should make it a formidable market.

But NYSE Vice Chairman John J. Phelan Jr. said the Big Board wants to enter the financial futures market not to grab anyone else's share of the market but rather to get in on an area that he said will continue to grow rapidly in years to come.

The big Board hopes to trade in many more than the seven contracts it initially proposed.

The New York Futures Exchange, as the Big Board subsidiary floor is to be called, would be located about a block away from the NYSE building on Wall Street and will open with three trading rings - one each for the Treasury securities and a third for the foreign exchange trading.

Investors engage in financial futures trading for the same reasons they buy and sell futures contracts for wheat or gold: Buyers seek to protect themselves against price increases and speculators want to anticipate profits on a price decline.

A miller who wants to protect himself against a rise in the price of wheat would buy a contract for delivery at some point in the future. A speculator who anticipates a price decline will promise to deliver wheat at a certain price and make money on delivery date if the wheat costs less.

The motivations are similar in financial futures trading. If interest rates rise (and, therefore the price falls), the speculator makes money.

In all futures trading there are as many winners as losers. If wheat prices rose, the miller protected himself and the speculator who promised delivery on a certain date loses. If wheat prices fell, the miller would have been better off waiting to buy his wheat but the speculator would make money.

In any event, buyers and sellers of futures contracts rarely make or receive a delivery of the commodity in question. They are almost always used as a financial hedge add the contracts are liquidated before the delivery date.

The Federal Reserve Board and the Treasury have been concerned that a proliferation of futures trading in government securities could make federal debt management more difficult. The agencies have urged the CFTC to make sure that there are enough Treasury securities around to insure that the securities can be delivered if need be.

The CFTC, in approving the contracts earlier this week, made sure that no two exchanges are trading in the same security.