* US stocks jump after Wall Street's worst day in 20 years
* Dollar rises over 2 pct vs yen; oil up over $4 a barrel
* Cautious optimism in markets despite bailout rejection
* Bonds fall as fresh hope for bailout cuts safety bid (Adds close of U.S. markets)
By Herbert Lash
NEW YORK, Sept 30 (Reuters) - The dollar surged and U.S. stocks jumped on Tuesday, recouping more than half the losses sustained from Wall Street's worst day in 20 years, on growing optimism Washington will find a way to rescue troubled banks.
In sign U.S. authorities are working to slow the heavy losses banks have taken on hard-to-price assets, regulators will provide guidance that will not use fire-sale prices to evaluate those assets, a document obtained by Reuters said.
In another encouraging sign for investors who suffered on Monday the biggest plunge on Wall Street since October 1987, President George W. Bush and lawmakers were working to revive a bill that sparked a steep sell-off after Congress rejected it.
The broad S&P 500 gained more than 5 percent, while the Nasdaq and Dow rose slightly less on the news. Monday's crash buzzed almost 9 percent off the S&P, and the two other indexes suffered nearly as much.
Oil rose more than $4 to rise over $100 a barrel on expectations a new financial stability plan would pass, while gold fell, weighed down by the rally in stocks and the dollar.
The stock rally spurred an unwinding of safe-haven bidding for U.S. government debt, pushing bond prices sharply lower.
The dollar jumped 2 percent against the yen <JPY=> and 3 percent against the Swiss franc <CHF=> at one point as cautious optimism built that Congress will eventually approve a $700 billion plan to bail out banks holding tainted assets.
Strong readings on U.S. consumer confidence and a measure of manufacturing activity in the U.S. Midwest also boosted equities and further curbed the appeal of debt. The two September reports tempered fears about the economy's health.
"All eyes are still on Washington," said Jim Dunigan, managing executive of investments at PNC Wealth Management in Philadelphia. "There are at least some hints of optimism that something will still happen soon with regards to the bill."
The Dow Jones industrial average <
> ended up 485.29 points, or 4.68 percent, at 10,850.74. The Standard & Poor's 500 Index <.SPX> closed up 58.48 points, or 5.29 percent, at 1,164.87. The Nasdaq Composite Index < > ended up 98.60 points, or 4.97 percent, at 2,082.33.However, for the quarter the Dow fell 4.4 percent, the S&P tumbled 8.9 percent and the Nasdaq shed 9.2 percent.
Investors snapped up beaten-down shares, with shares of financial companies, including JPMorgan Chase <JPM.N>, up almost 14 percent, among the standouts.
Technology shares also bounced back, with Apple Inc <AAPL.O> the top boost on Nasdaq, a day after the tech-rich index posted its worst day since April 2000 when the dot-com bubble burst. Apple gained nearly 8 percent.
Talk that U.S. lawmakers may reach some kind of agreement by the end of the week and speculation that central banks could slash interest rates tempted investors back into markets.
"I do think that Congress will pass the bailout package, possibly before this weekend," said Mark Waggoner, president of Excel Futures in Huntington Beach, California.
European shares closed higher on Tuesday, bouncing from Monday's 3-1/2-year closing low.
The FTSEurofirst <
> index of leading European shares ended up 1.59 percent at 1,063.65. Banks added the most points to the index, with HSBC <HSBA.L> up 4.2 percent and Standard Chartered <STAN.L> jumping 8 percent.With a rescue plan still in limbo, borrowing costs in the interbank market soared in overseas trading, as financial companies scrambled for funds to meet quarter-end needs.
Some rates subsided in response to large liquidity injections by the Federal Reserve and European Central Bank.
The yield on the London interbank offered rate (Libor) on overnight dollar funds jumped the most in any day on record, rising to 6.87 percent, according to Reuters data. It was the highest Libor rate, a reference point for trillions of dollars in consumer and corporate debt, in at least 7-1/2 years.
A goal of the bailout is to thaw credit markets, lower borrowing costs and unleash funds to banks, companies and consumers.
U.S government debt fell.
The benchmark 10-year U.S. Treasury note <US10YT=RR> fell 2-4/32 to yield 3.84 percent, and the 2-year U.S. Treasury note <US2YT=RR> fell 22/32 to yield 1.98 percent.
U.S. crude <CLc1> settled up $4.27 to $100.64 a barrel, after losing $10.52 on Monday in the second-biggest fall since April 23, 2003. London Brent crude <LCOc1> traded up $4.19 to settle at $98.17 a barrel.
Spot gold prices <XAU=> fell $24.45 to $878.80 an ounce.
December gold futures <GCZ8> settled down $13.60 at $880.80 an ounce in New York.
The dollar gained against a basket of major currencies, with the U.S. Dollar Index <.DXY> up 2.34 percent at 79.493.
The euro <EUR=> fell 2.34 percent at $1.4078, and against the yen, the dollar <JPY=> rose 2.19 percent at 106.31.
Asian stocks fell, chalking up the biggest monthly decline in more than a decade, but didn't match Monday's meltdown on Wall Street. Japan's Nikkei share average <
> closed down 4.1 percent to a three-year low and the MSCI index of Asia-Pacific stocks outside Japan <.MIAPJ0000PUS> fell 2.73 percent. (Reporting by Ellis Mnyandu, Chris Reese, Nick Olivari and Richard Leong in New York and Jessica Mortimer, Brian Gorman, Alex Lawler and Jane Merriman in London; Editing by James Dalgleish)