NEW YORK, NOV. 11 -- The dollar rose against key currencies today, boosted by optimism among traders that the U.S. trade deficit will show a small improvement over August's $15.7 billion figure.

The foreign exchange desk at Bear, Stearns & Co. said the dollar finished at 1.6748 West German marks, up from Tuesday's close of 1.6655.

Exchange quotes from commercial banks were unavailable because most banks were closed for the Veterans Day holiday; many brokerage houses operated foreign exchange desks with skeleton staffs.

Earlier, in Frankfurt, the dollar ended at 1.6755, up from Tuesday's all-time low of 1.6530.

Against the Japanese yen, the dollar ended at 135.13, up from 134.70 Tuesday.

In Tokyo, the dollar finished at 134.35 yen, up from its Tuesday close of 133.40, which also was a record low.

Bear, Stearns foreign exchange trader Simon Fisher said many traders expect improvement in September's U.S. trade deficit, slated for release Thursday. This expectation helped the dollar today, he said.

The dollar moved sharply lower after release of the August data, which was termed disappointing by many traders.

Bear, Stearns is predicting a September trade deficit of $15 billion, Fisher said, adding that the market consensus is that it will come in at about $14.7 billion.

Throughout the day the market was also cheered by reports indicating that President Reagan and members of Congress may be reaching an accord over the U.S. budget deficit, Fisher said.

The dollar fell to $1.3167 Canadian from $1.3182.

The British pound ended at $1.7785 in New York, down from its close on Tuesday at $1.7855. Earlier in London, the pound fell to $1.7795 from its Tuesday close at $1.80.

Overseas traders said the dollar rebounded in Europe and Japan when markets there learned of Reagan's Tuesday remark that he wants no further decline in the value of the American currency.

They said the remark calmed the market temporarily, but failed to clarify the administration's policy on the dollar. It is unclear if the remark will have any long-term effects, traders said.

Other European closing rates with late New York prices and comparable Tuesday rates in parentheses:

Zurich, 1.3727 Swiss francs vs. 1.3527, a record low (1.3750 vs. 1.3655); Milan 1,227.00 Italian lire vs. 1,220.50 (1,238 vs. 1,226.50).

Republic National Bank in New York closed cash gold at $462.25 an ounce, up from $461.50 Tuesday. New York's Commodity Exchange settled the spot contract at $461.90, up from $461 on Tuesday.

Earlier in London, gold finished at $462.25 an ounce, up from its $458.25 close Tuesday. But in Zurich it fell to $462.50 an ounce, down from $468 Tuesday.

Silver rose to $6.56 an ounce from $6.52 on the cash market. The Comex settled silver at $6.547 an ounce, up from $6.505 on Tuesday. Earlier in London, silver rose to $6.60 an ounce from $6.38.