EMERGING MARKETS-Brazil's real jumps 3.5% as Bolsonaro's strong showing spurs policy cheer

* Brazil's real set for best session since Oct 2018 * Colombia's peso jumps more than 1% as oil rallies By Susan Mathew Oct 3 (Reuters) - Brazil's real jumped 3.5% on Monday and stocks were on course for their best session since December as investors cheered far-right President Jair Bolsonaro's stronger-than-expected showing in the first round of a presidential election. Most other regional stocks and currencies also rallied, as U.S. stocks jumped and the dollar steadied. As OPEC+ considered its biggest output cut since 2020, crude prices surged more than 5%, lifting currencies of exporters such as Mexico and Colombia, with the latter moving 1.3% away from near three-month lows. Sentiment had been hit earlier in the day as dismal factory activity data from around the globe heightened worries about economic growth. Risk assets have been hammered this year as major central banks tighten policy to curb surging inflation but at the risk of tipping economies into recession. Latam gains helped broader EM indexes cut a majority of their session losses, as did gains in South African and Turkish assets . ELECTION ZEAL Brazilian markets rallied after Bolsonaro's leftist challenger, former President Luiz Inacio Lula da Silva, fell short of clinching victory in a first round of voting on Sunday. Lula's advantage of 5 percentage points was tighter than most polls had shown and, along with a strong showing for the right in Congress, set the stage for a highly competitive and tense second round on Oct. 30. "Such a run-off reassures the market that market-leaning policies tend to be more likely," said Mauricio Une and Renan Alves, strategists with Rabobank. Brazil's foreign currency bond spreads over U.S. Treasuries narrowed 17 basis points to 282 bps. The real looked to log its biggest one-day jump in more than four years and the main stock index surged 4.0%, also lifted by an 8.5% in privatization candidate Petrobras. "We expect Lula to announce at least part of his economic team and present a draft of his economic proposal (during the campaign)," said Elizabeth Johnson, MD Brazil research at TS Lombard. "Although he is unlikely to name a Finance Minister ahead of the second round, we expect him to announce a market-friendly team, which could include former Banco Central President and Finance Minister Henrique Meirelles. This could further support Brazilian assets." Elsewhere, Hungary's forint hit record lows against the euro on worries over EU funds and Europe's energy crisis hitting hard and after the central bank signalled the end of sharp interest rate hikes. Key Latin American stock indexes and currencies: Stock indexes Latest Daily % change MSCI Emerging Markets 874.78 -0.12 MSCI LatAm 2177.81 6 Brazil Bovespa 114452.38 4.01 Mexico IPC 44978.74 0.79 Chile IPSA 5121.44 0.14 Argentina MerVal 143180.92 2.923 Colombia COLCAP 1143.60 1.36 Currencies Latest Daily % change Brazil real 5.2097 3.53 Mexico peso 19.9820 0.79 Chile peso 956.9 1.05 Colombia peso 4549.68 1.20 Peru sol 3.982 -0.18 Argentina peso 148.2200 -0.61 (interbank) Argentina peso 283 1.77 (parallel) (Reporting by Susan Mathew in Bengaluru; Editing by Kirsten Donovan)