Boston Stock Exchange bounces out of a stodgy corner.

Just three years ago, the stodgy Boston Stock Exchange could barely manage trading within its tiny four walls. It was floundering in almost $1 million of red ink.

Today, it's on the verge of the first floor-to-floor satellite link with a foreign stock exchange - across the border in Canada. And trading in Beantown has never been better.

The ebullient architect of this dramatic recovery and the overseas gambit is Charles J. Mohr. An 11-year veteran of the New York Stock Exchange, he fidgets through an hour-long interview like a floor trader handcuffed during a late-afternoon rally. But it's this energy and his Wall Street savvy that have returned Boston to profitability, observers say.

While the pundits in New York are talking about how to fend off or adapt to the growing international competition in the securities industry, Mr. Mohr is already making his move. In less than a month, he hopes to make a Montreal connection.

The electronic tie-in would provide Boston with a fresh revenue source, and foreign brokers would see a sharp drop in the cost and time delay of trading United States stocks.

Mohr isn't planning to stop with Canada, either.

''Let's say I go over to the Frankfurt Stock Exchange, where a lot of their members deal in US securities,'' he says. ''I put in a terminal, and any member of the Frankfurt exchange can go up to it and put in an order for 500 shares of IBM. ... Within four seconds it reaches my floor. I execute the order. I charge the member - ABZ Securities of Dusseldorf - 2 cents a share, vs. the 9 cents he's been paying. And I give him a report back in 30 seconds, instead of 10 minutes.''

Typically such a foreign transaction would have to go through a US brokerage that charges twice what it collects from domestic traders, Mohr says. A report back can take as long as 30 minutes.

Mr. Mohr has plans for a European link, possibly London, by year's end: ''Most other exchanges are focusing on futures and options. ... In my mind, the future is in the international market. There are lots and lots of countries that would love to be able to do this.''

Such vision, and some hard-nosed management, have enabled Mohr to bring the Boston exchange back from near-extinction.

''In a short period of time, they've come back a long way,'' says Willis Riccio, regional administrator of the Securities and Exchange Commission. At one point, the SEC was concerned that the exchange, occupying a plush 38th floor in downtown Boston, would go belly up.

''Basically it was bankrupt,'' Mohr agrees. ''The place was a literal mess. It ran reasonably well up to 1974 or '75. But over the next six or seven years, when the industry changed and volume picked up, it was a real mess.''

To mop up, Mohr cut the staff from some 240 to 130. He began automating, upgrading with new equipment, and dropping unprofitable operations.

But he dismisses these steps with a wave of a hand. ''Sure we fired people and automated, but to get to that point is a process of management ... this place had no management structure at all. There used to be four entities, four presidents, four boards. No one knew whom to report to, no one identified problems, no one could suggest solutions.

''Then the auditors came in and discovered the 15 major disasters that had occurred during the year, and the board would ask, 'How could this happen?' ''

After cleaning house, Mohr had to lure the financial community back to his door. And he has been largely successful in reeling in trades from the major brokerages, including Merrill Lynch, Prudential-Bache, E. F. Hutton, and Fidelity.

Mohr has capitalized on his background at the NYSE by restructuring and selling Boston against the Big Board's weaknesses.

For instance, the size of the NYSE makes it the preferable exchange for block trades (10,000 shares and up). Regional exchanges tend to excel in small to medium-size trades. The Philadelphia Stock Exchange is noted for its automated order system of fewer than 400 shares. Boston now guarantees execution of trades up to 1,299 shares (vs. a guarantee of 600 shares or fewer at most exchanges). And there are plans to raise that to 1,599 or 2,099 shares in the next month or two.

A diminutive exchange does have its advantages, Mr. Mohr asserts. Some 45 traders are elbow to elbow along counters jammed with computer terminals on Boston's split-level trading floor. The result: ''We can call across the floor and execute a trade here in 30 seconds. In New York, you can spend five minutes getting across the floor.''

The city of Boston is flush with banks, insurance companies, and other institutional investors, and Mohr says he would be pleased if the Boston exchange saw 5 percent of the stock trades that go to New York. But even in this year's mostly declining market, trading has been relatively brisk.

''Eighty percent of the brokerage firms lost money starting in January, and we didn't lose a thing. As a matter of fact our trade levels increased in May, June, and July - primarily because we've been able to bring new customers aboard ,'' Mohr says.

''Charlie has done a super job,'' says Arthur J. Stavaridis, a vice-president at Prudential-Bache and a member of the BSE board. Pru-Bache has upped its trading here, and ''we wouldn't do it if prices and executions weren't competitive.''

But Stavaridis admits, ''We don't send them a major portion of our business.'' Mohr still has a selling job to do. Some brokerages contacted had doubts about Boston's competitiveness and said they didn't want to go throught the hassle of diverting trades to Boston from New York. Mohr admires the way the Philadelphia Stock Exchange has raised its volume by setting up a separate subsidiary for trading options.

''On pure natural volume, I beat Philly every day. ... But over half their stock volume is done by options-offset business.'' That is, when a stock options contract is sold, the marketmakers will buy shares of that stock to hedge against the option. And he says, ''Philly's pricing structure makes it financially impossible to do the (stock side of the) trade elsewhere.''

Mohr is already angling for a piece of the options action. He expects to know by November whether the SEC will grant the Boston exchange - or the National Association of Securities Dealers or some other exchange - permission to trade over-the-counter stock options. (First, the SEC must decide if it will allow OTC options trading, but most observers expect a green light on this.)

Says Mohr: ''So far the Justice Department, the Securities Industry Association, and our good ol' buddies at the NYSE have supported our entry into this - which has made our bid significantly more serious than anyone thought three months ago.''