Shares in SpaceX have rocketed above its Nasdaq IPO price. © Reuters(Reuters) -- Shares of Elon Musk's SpaceX climbed more than 14% on Tuesday, lifting its valuation past Amazon.com and briefly above Microsoft to rank it among the top-five most valuable companies within days of a blockbuster debut.Shares of the rockets-to-AI company were last up 14.3% at $220, jumping more than 62% above the $135 IPO price and giving the company a market capitalization of around $2.85 trillion if gains hold. The stock gave the biggest boost to the Nasdaq Composite index.Amazon's valuation stands at $2.64 trillion. SpaceX also briefly topped Microsoft's valuation of $2.92 trillion. The world's top three companies, meanwhile, exceed $4 trillion in market value.SpaceX options also began trading, offering investors another avenue to bet on the future of the newly listed shares."Today the SPCX options launch, offering standard monthly expiration and strikes ranging from $25 to $380. If call demand is heavy, dealers might be forced to buy SPCX into this low-liquidity situation," said Brent Kochuba, founder of option analytics platform SpotGamma."Starting next week we may see index demand increase, with more shares not slated to be made available for 1-2 months."Analysts and portfolio managers said investors should brace for volatility, particularly early on in SpaceX's life as a public company, due to its relatively small float and high valuation."We can say with certainty that this valuation makes absolutely no sense today. People are buying SpaceX in the expectation that others will buy too and push the price higher -- that's speculation," said Ipek Ozkardeskaya, senior market analyst at Swissquote Bank.The company reported sales of $18.67 billion last year and a net loss of $4.94 billion after merging with money-losing xAI -- in contrast to many of Wall Street's big technology companies that have posted bumper numbers.The rally could continue as SpaceX is set for fast-track inclusion in the Nasdaq 100, which will soon make it a major holding for passive funds and ETFs that track the index, creating a fresh source of demand for its shares.FTSE Russell and MSCI are also set to add the stock to their indexes, effective June 26 and June 29, respectively."While index inclusion alone is typically insufficient to drive sustained repricing, we see the combination of passive flows, with a "buy" rating.SpaceX also said on Monday that its underwriters had exercised the "greenshoe" option to purchase additional shares, increasing the total proceeds from its initial public offering to $85.7 billion from $75 billion that it raised last week.More than $23.1 billion worth of SpaceX shares exchanged hands as of 10:07 a.m. ET, which was several times the trading volumes in Nvidia, Microsoft Tesla and Apple combined.Other heavyweight technology stocks, including Nvidia and Microsoft, were trading slightly lower.Earlier in the day, SpaceX also said it would acquire software company Anysphere for $60 billion.