The Holding companies for the nation's three largest banks - Bank America Corp., Citicorp and Chase Manhattan Corp. - said yesterday that higher interest rates and loan volume had contributed to greatly improved earnings in the third quarter.

BankAmerica, holding company for SanFrancisco-based-Bank of America, the nation's largest, said income in the quarter was $147.3 million ($1.01 a share) compared with $110.4 million (76 cents) a year ago.

Citicorp, which owns No. 2 Citibank, said earnings were $119.1 million (95 cents a share) in the period, up 36 percent from the $87.8 million (70 cents) reported a year ago.

Third-ranked Chase Manhattan reported a larger gain, saying that income was $50.3 million, up 62 percent from the $31.1 million earned in last year's third quarter. Per-share earnings were $1.41 compared with 91 cents a year ago.

The three banks also reported improved profits for the first nine months of the year. The banking business has been very strong this year as the benefits of heightened by steadily rising interest rates.

The prime lending rate, the interest banks charge their best customers, stands at 10 percent, its highest point in nearly four years. The prime rate was then 7 3/4 percent on Jan 1.

Bank America's nine-month profits were $368 million ($2.52), up from $286.3 million ($1.97) a year earlier; Citicorp's rose to $363 million ($2.93) from $288 million ($2.30); and Chase's were $138.5 million ($3.92) compared with $87.1 million ($2.65) in the 1977 nine month period.

Benefiting from record stock market volume in recent months, Merrill Lynch & Co. Inc., the nation's largest brokerage house, posted third-quarter earnings and revenues nearly triple levels of a year earlier for the best quarter in the company's history.

Merrill Lynch said net income in the quarter was $32.4 million (90 cents a share) compared with $11.1 million (32 cents) a year ago.Revenues were $433.7 million, up from $296.2 million a year ago.

Merrill Lynch said earnings and sales for the first nine months of the year were also up considerably, reflecting the extremely heavy activity this year in the stock market.

Nine-month profits were $62.3 million ($1.74) on revenues of $1.12 billion compared with 1977 nine-month profits of $36.1 million ($1.03) on $819.7 million in revenue.

Merrill Lynch said commission revenues increased by 82 percent in the third quarter, with commission revenues on listed securities, options and commodities all showing sharp gains.

Republic Steel Corp's third-quarter earnings tripled to $30.6 million ($1.89 a share) from $10 million (62 cents) in the same period last year.

Republic said earnings in the 1977 quarter were depressed by a lengthy iron ore workers strike, by wildcat strikes at the company's coal mines and by a fire at its Mahoning Valley plant.

For the first nine months, Republic's net income totaled $71.7 million ($4.43) compared with $26 million ($1.61) during the corresponding 1977 period.

Sales during the third quarter totaled $869.1 million compared with $751.3 million for the corresponding 1977 period. Sales for the first nine months totaled $2.6 billion compared with $2.2 billion a year earlier.

"While earnings have improved over the same period last year, they are only 2.7 percent of sales and represent a return on equity substantially below the average of all manufacturing companies," said W.J. DeLancey, Republic's president and chief executive officer.

He said steel consumption continues at a high level, but imports could reach 2 million tons this year, the highest level in history.

Trans World Airlines, enjoying record passenger volume in recent months, with the rest of the airline industry, said yesterday that third-quarter earnings had risen 17.8 percent and income for the first nine months of the year was nearly double last year's record.

The airline said third-quarter earnings were $83.5 million ($5.03 a share) compared with last year's $72.6 million ($4.45). Revenue in the period was $1.04 billion, up from $943 million in the third quarter of 1977.

The nine-month earnings figures were $95.1 million ($5.26) compared with $50.1 million ($8.12), although revenue was up only slightly from last year.

Philip Morris Inc. reported a 22 percent rise in profits to $115.18 million ($1.91 a share) in the third quarter from $94.14 million ($1.57) a year ago on a gain in sales to $1.817 billion from $1.376 billion.

Nine-months profits were $307.02 million ($5.12 a share on sale sof $4.88 billion compared with $250.71 million ($4.19) a year earlier when nine-month sales were $3.848 billion.

Chairman Joseph Cullman III said both domestic and international cigarette sales and sales of the Miller Brewing subsidiary were strong.

And the Jos. Schlitz Brewing Co. reported earnings of $4.59 million (15 cents a share) for the third quarter of 1978 compared with $6.86 million (24 cents) during the same period last year. Shipments were down from 5.9 million to 5.4 million barrels, the company said Monday.

But the Milwaukee-based brewer reported sales were up slightly from $299 million to $302.93 million during the quarter.

Nine-month earnings were $13.19 million (45 cents) compared with $24.59 million (85 cents) at the same point last year. Sales of $857.81 million compared with $907.80 million.

American Cynamid Co. had a 12.9 percent gain in third-quarter earnings to $36 million (75 cents a share) from $31.9 million (67 cents) a year ago. Sales rose to $672.5 million from $604.6 million.

Nine-month profits were $112 million ($2.34) on sales of $2.01 billion compared with $102.8 million ($2.)115 a year earlier on sales of $1.77 billion.