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Trending tickers: Coinbase, Alibaba, Tesla, NatWest and Vistry
Other cryptocurrencies also continued to rise, including smaller digital tokens such as dogecoin (DOGE-USD), on expectations of more favourable regulation around the space.
Trump had pledged during in his campaign to make the US "the crypto capital of the planet" and to accumulate a stockpile of bitcoin.
The latest rise in cryptocurrencies comes as the Republican party moves closer to taking overall control of US Congress.
The surge in these digital tokens over the past week has driven shares in cryptocurrency exchange platform Coinbase higher, with the stock closing Friday's session up nearly 6%.
Shares in e-commerce firm Alibaba were flat on Monday, as China's lagging economy dampened enthusiasm around the Singles' Day shopping festival.
The annual event, which had started out as a one-day event on 11 November, sees retailers offering large discounts to lure in shoppers.
However, this year's event has been overshadowed by concerns around China's sluggish economy. Stocks in Asia's markets were down on Monday, after stimulus measures announced by China's authorities disappointed investors.
China's National People's Congress Standing Committee announced a 10 trillion yuan ($1.39tn) debt package after markets closed in Asia on Friday.
Russ Mould, investment director at AJ Bell, said that "what has been announced so far doesn’t seem to be moving the needle and the risks to China from a second Trump presidency are now overshadowing efforts to get the economy moving".
"The question on investors’ lips will be whether this encourages Beijing to unveil a bolder package of measures," he said.
Investors will also be looking for more signals on consumer demand in China in Alibaba's latest set of quarterly results, due out on Friday 15 November.
Musk had a been a major supporter of Trump's campaign, with Wall Street analysts believing that his policies could benefit Tesla.
Wedbush analyst Dan Ives said in a note last week that Trump could roll back the current electric vehicle (EV) tax incentives in place and be "an overall negative for the EV industry." But given Tesla's potential competitive advantage in the EV space, this could be a "huge positive" for Tesla.
"Tesla has the scale and scope that is unmatched in the EV industry, and this dynamic could give Musk and Tesla a clear competitive advantage in a non-EV subsidy environment, coupled by likely higher China tariffs that would continue to push away cheaper Chinese EV players, such as BYD (1211.HK) and Nio (9866.HK), from flooding the US market over the coming years," he said.
Bank NatWest has bought back ￡1bn of its shares from the UK government, according to an announcement on Monday.
The government and NatWest said that this sale meant that the Treasury's stake in the bank would fall to around 11.4% from 14.2%.
The announcement also said that the government would "keep further disposal options under consideration when market conditions permit and it is value for money to do so".
Following bailouts in the financial crisis, the government at one point had an 84% stake in the bank, which was previously known as the Royal Bank of Scotland.
In a separate statement on Monday, Paul Thwaite, CEO of NatWest Group, said: "This transaction represents another important milestone on the path to full privatisation.
"We believe it is a positive use of capital for the bank and for our shareholders and we are pleased with the sustained momentum in reducing HM Treasury's stake in NatWest Group throughout this year."
Housebuilder Vistry started Monday's session as the biggest riser on the UK's FTSE 100 (^FTSE) index, recovering slightly from a drop in its share price on Friday, after cutting full-year guidance.
Vistry lowered its pre-tax profit guidance from ￡350m to ￡300m, as more details came to light around its cost issues in its South division.
Aarin Chiekrie, equity analyst at Hargreaves Lansdown, said: "An independent review found that the issues in the South stemmed from insufficient management capability, non-compliant forecasting processes and poor divisional culture.
"This highlights the pressure being felt internally to navigate the operational changes as the group’s new business model finds its feet."
Other companies in the news on Monday 11 November:
