A man walks past a Bitcoin poster in Hong Kong, April 15. AFP-Yonhap

After Donald Trump's victory in the U.S. presidential election, the crypto market has been setting new record highs daily.

Bitcoin surpassed $80,000 for the first time around 7 a.m. on Sunday, continuing its strong upward momentum and reaching an all-time high of $81,534. After a brief pause on Monday, it shows no signs of slowing down.

Ethereum, another leading cryptocurrency, crossed the $3,000 mark on Sunday. It is trading above $3,200 after climbing over 6 percent on Monday. Dogecoin — a meme coin that Tesla CEO Elon Musk has actively promoted — also spiked by more than 40 percent.

Trading volumes of Bitcoin and Ethereum spot exchange-traded funds (ETFs) have skyrocketed as well. The total assets of Bitcoin spot ETFs have even reached $34.3 billion, surpassing the $33 billion held by BlackRock's Gold Trust Exchange Traded Fund (ETF), the largest gold ETF.

As investor sentiment strengthened, cryptocurrency-related stocks also rallied across the board in the Korean stock market on Monday.

Hanwha Investment & Securities, which holds shares in Dunamu (the operator of Korea's largest crypto exchange, Upbit), traded at 4,145 won ($2.97), up 16.76 percent from the previous session. For the same reason, Woori Technology Investment rose 7.28 percent. TSCIENTIFIC, a stakeholder in Bithumb's operating company, surged 9.77 percent, while blockchain firm Galaxia Moneytree climbed 6.52 percent.

The boom reflects market enthusiasm following Trump's election victory.

During his campaign, Trump declared that he wanted the U.S. to become the "crypto capital of the planet" and the "Bitcoin superpower of the world." He has pledged to appoint a regulator with deep expertise in digital assets within his first 100 days in office and to dismiss Securities and Exchange Commission Chairman Gary Gensler, who has enforced strict regulations on virtual assets.

Market insiders anticipate continued growth under the Trump administration, with relaxed regulations and industry autonomy.

A "Red Sweep," where the U.S. Republican Party gains control of both the Senate and the House in addition to the White House, is also becoming a reality. This shift would likely give a significant boost to bills proposed by the Republican Party, according to Hashed Open Research.

For instance, Senator Cynthia Lummis reaffirmed her commitment to advancing crypto legislation following Trump's victory. Lummis, who attended the Bitcoin Conference in Nashville with Trump, proposed a law on July 31 to incorporate Bitcoin as a U.S. national strategic asset.

The U.S. Federal Reserve's consecutive policy rate cuts have further benefited the cryptocurrency market.

Some market predictions indicate that the price of Bitcoin could soar above $100,000 by the end of the year.

Nick Philpott, co-founder of Zodia Markets, said he expects ETF and broader crypto inflows to push the price to $100,000 by early next year, if not sooner. Geoff Kendrick, global head of digital assets research at Standard Chartered, also forecasts the price of Bitcoin to reach $125,000 by Trump's inauguration at the latest.

However, with the sharp rise in Bitcoin and most other coins, some caution that a short-term correction may be on the horizon. Altcoins, in particular — being more volatile than Bitcoin — tend to see steeper declines during market corrections.