By Christine Kim

SEOUL (Reuters) - The window for more monetary easing in South Korea looks to have closed after the U.S. Federal Reserve's rate rise even as Asia's fourth-largest economy struggles with high household debt and fallout from the scandal that toppled President Park Geun-hye.

U.S. rates are now within half a percentage point of Korea's benchmark rates, and on current projections could be level by the end of the year for the first time in a decade.

While Wednesday's Fed rate rise won't trigger immediate capital flight, there are risks from letting South Korea's yield premium over the United States narrow too much, or even turn negative, when markets expect the U.S economy to improve and rates to rise further.

"The BOK will find it difficult to cut rates now," said a financial authority with knowledge of monetary policy thinking.

"They won't be able to hike immediately though; they'll likely wait until year-end to observe the economy."

Since mid 2016, as inflation has crept up to the BOK's 2-percent target, yields on 1-year and 3-year treasury bonds have slipped below their U.S. counterparts on occasion.

As of Wednesday, the yield for 3-year Korean government bonds stood at 1.759 percent, a shade higher than 1.5980 for U.S. 3-year treasury bonds.

Stephen Lee, chief economist at Meritz Securities in Seoul said the opportunity for the BOK to cut rates is "long gone", and thinks the central bank will have to raise rates in 2018.

Domestic activity is struggling. Consumption remains weak, weighed down by high levels of household debt, a cooling property market, rising unemployment and the political and corporate scandal that culminated in Park's impeachment last week.

"I don't think they'll do it immediately but if the economy normalizes, the historical pattern is the BOK will eventually follow the Fed," said Cliff Tan, East Asian Head of Global Markets Research at Bank of Tokyo-Mitsubishi UFJ.

"By the time we get to (U.S. rate hike) number four, there will be some consideration to follow the Fed."

Wednesday's rise was the third since the Fed began lifting rates in December 2015, taking the target for the overnight rate to a range of between 0.75 percent and 1.00 percent.

For now, a strong external performance is supportive for foreign investment. Exports grew at their fastest annual pace in five years in February, reinforcing the buffers of a large current account surplus and hefty foreign exchange reserves.

Foreigners held 96.08 trillion won ($84 billion) of South Korean bonds at the end of February, after South Korea saw the biggest bond inflows since 2009 that month.

But that followed bond outflows worth 7.6 trillion won through the final five months of 2016 ahead of the Fed's December rate rise.

Also, following U.S. President Donald Trump's election, a more protectionist environment carries heavy risks for South Korea's export reliant economy.

Another factor pointing to an end of South Korea's easing cycle is the presidential election called in the wake of Park's impeachment, as it could lead to greater government spending.

"From a policy perspective, if the past is any guide, newly elected governments have tended to utilize fiscal policy aggressively at the start of their five-year terms," economists at J.P. Morgan said in a research note on Tuesday.

"This in turn raises the possibility that fiscal policy would turn sharply in the second half, no matter which party wins in the election. This fiscal shift also reduces the need for monetary policy accommodation," they said, removing their previous call for a rate cut.

(Editing by Simon Cameron-Moore)