Whether something or anything has intrinsic value or not is philosophical, a matter of opinion and has been debated for centuries.
https://plato.stanford.edu/entries/value-intrinsic-extrinsic/#WhaHasIntVal
With regards to Bitcoin, I don't think one can differentiate between its intrinsic or market value to determine if it's trading at a premium or discount. Technical analysis would probably be the next best option due to the speculative nature of the asset.
With regards to market value, I think there's a synergy of factors that contribute towards it. These include:
1. Its use as a non-inflationary store of value and better alternative to gold.
2. Scarcity and difficulty in creation.
3. The ability to control it, move it around freely and trade it without third party intervention and with minimal delays and transaction fees.
4. Expected price appreciation. The market expects ts value to keep rising due to its increasing scarcity and evolution so it represents a better investment alternative to storing fiat money in a savings account or fund earning low interest.
5. Its new technology, millennials and an ever increasing amount of early adopters immediately embrace new technology that gives them more control and convenience over their lives.
6. Anti-government and institutional sentiment post GFC.
7. It's decentralized, secure and more private (debatable for Bitcoin) than other forms of payment.
8. It's easily accessible and supported by all the exchanges so can be easily traded with other currencies and with minimal delay. There's none of the excessive red tape you get with regulated markets.
9. Barriers to entry are almost non-existent, doesn't require significant capital
10. One can quickly and easily build a portfolio without paying the excessive fees usually associated with share purchases. You don't need to purchase equipment or a platform licence to actively trade it.
11. When trading it, there's no intermediaries, brokers or market maker and no conflict of interest.
12. It has the largest market capitalization and highest daily trading volume. More exposure seems to translate into a higher value. This was seen with Monera just recently.
13. It's viewed as the most stable cryptocurrency making it the most trusted by counterparties.
14. It has the largest number of miners and hash power directed towards mining it.
15. It's becoming more accepted in online retailing as a form of payment e.g newegg.
16. Strong brand name and public perception.
In a nutshell, there's a competitive market for it now, volume and interest has increased exponentially which is driving its market value and promoting its evolution towards becoming a standard form of online payment, store of value and unit of account. You could probably argue there's bit of self-fulfilling prophecy going on because the market wants the technology to succeed whether it currently offers actual, quantifiable value in an economics sense or not.
It worth 4500 USD because that's its market value based on market capitalization and number of coins in circulation.