The Jakarta Composite surged to a fresh 15-month high Friday morning after Joko Widodo was confirmed as president of the world's third-largest democracy.

Stocks powered to a high of 5223.975 in early trade before falling slightly, while the rupiah (Exchange:IDRUSD=) strengthened 0.3 percent to 11,662 rupiahs per U.S. dollar (New York Board of Trade (Futures): =USD) after Indonesia's highest court upheld the July election result on Thursday. The result was in question after losing candidate Prabowo Subianto claimed that Joko Widodo - commonly known as Jokowi- cheated.

Whether or not upward momentum continues depends on Jokowi's ability to push through promised reforms, according to Seng Wun Soon, regional economist at CIMB (Kuala Lumpur Stock Exchange: CIMB-MY) bank.

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"A lot of the optimism and euphoria about Jokowi's victory has already been priced in to the market," said Soon.

Indonesian stocks are up 22 percent year-to-date, while the rupiah has rallied around 4 percent against the dollar.

"Going forward valuations are not as attractive...I would be a bit cautious... and now it's about markets keeping a close eye on Jokowi and making sure he delivers on other measures like reforms and other things that will boost the economy," added Soon.

Other analysts told CNBC that Jokowi's confirmation could boost the nation's stock market and currency further.

"The latest development could boost the rupiah and the Jakarta Composite Index in the interim. We've started to see some positive sentiment in the currency," said Ryan Huang, strategist at IG (London Stock Exchange: IGG-GB).

Huang noted that the rupiah consolidated a bit against the dollar over the past month as the courts deliberated the contested election result.

"With that out of the way and less political uncertainty now, we'll be watching out for a breakout and whether dollar-rupiah will weaken towards its next support level. That could be the case if it breaks below the 11,722 support level and test its next support at 11,500," added Huang.

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Challenges ahead

Jokowi and his Indonesian Democratic Party of Struggle (PDI-P) will officially take office on October 20 and will need to hit the ground running.

Indonesia faces a number of pressing economic issues, including a ballooning fuel subsidy costs and a widening current account deficit. Jokowi will also have to tackle the country's dilapidated infrastructure system, widespread poverty and deeply ingrained corruption.