Is it possible to buy and sell bitcoin without any of the exchanges knowing about it? Since the price of bitcoin is determined by people buying and selling, could these secret exchanges cause the reported values to be different from reality?
Is it possible to buy and sell bitcoin without any of the exchanges knowing about it?
Absolutely, you can send cryptocurrency from one wallet to another without anyone knowing what you are getting in return for it. The exchanges only know about the transactions they facilitate or have shared with them.
...could these secret exchanges cause the reported values to be different from reality?
No, it's still reality, it's just a different exchange rate based on the environment the transaction occurs in. Even then, most people value their cryptocurrency in terms of their local currency or USD so most likely the prices people settle on for direct cryptocurrency payments are based on the rates reported by popular exchanges.
People using cryptocurrency to launder money might pay a premium, but it's a premium relative to the going rate for legitimate uses.
If the volume of fiat to cryptocurrency transactions was very small then an exchange-reported rate could become less useful.
Since people are still buying and selling Bitcoin at the exchange price on the exchange, the exchange price still reflects the actual Bitcoin price.
If the exchange price didn't reflect the actual Bitcoin price, people would buy or sell until it did! If a bitcoin is worth $39738 but the exchange lets me buy one for $39000 then of course I'm going to buy as much of a bitcoin as I can afford, and then sell it to someone else for $39738. Other people know this so they won't sell me one for $39000.
That's why there's just one "actual price" and all exchange prices must be near it.
As you pointed out, you might pay extra if you need to keep your bitcoin purchase secret. But don't think of that as part of "the price of a bitcoin". Instead think of it as a transaction fee from the person you're buying it from, which could be higher than normal because you are buying secrecy. Similarly, slight differences between different exchanges can be thought of as if the exchanges are not perfectly accurate in tracking "the" bitcoin price.
Those transactions are commonly called OTC, or Over The Counter.
Majority of transactions are OTC in crypto, and similarly in the regular stock market as well.
That means the price based on public exchanges represent only a small fraction of all the transactions.
Naturally if all OTC transactions were made publicly on exchanges, the price would be different.
It's a reason why in the early days, people posting large sell orders on exchanges were frowned upon because they were hurting the price and it was deemed selfish. Instead it was preferred to sell large amounts privately.
A good read on the topic for crypto by Circle Research: https://medium.com/circle-research/how-does-crypto-otc-actually-work-e2215c4bb13
Yes; you can sell your Bitcoins to your neighbor and no exchange will know the price you two agreed on.
More relevantly, large traders not-uncommonly form "private markets", or "dark pools", to liquidate large holdings where trades are done in much larger blocks than public exchanges handle. This is done to avoid or minimize price changes during the sale as a result of the sale. But, generally, these markets have been shown to be efficient; therefore, public markets are a good representation of an asset's value.
Any transfer of bitcoin has to put in the public ledger (unless there's some sort of escrow account or something complicated like that), so if the exchanges want to find out about it, they can (although they won't know what price was paid for it).
could these secret exchanges cause the reported values to be different from reality?
What is "reality"? If you mean "net present value of bitcoin", there's no guarantee that the exchange price will reflect that, and given the volatility of bitcoin, it clearly has deviated from the NPV quite often.
If you mean "fair market value", the exchange price is by definition the market price. There is no objective "right" price of anything. When people say "price", they generally mean the market price, so what the exchanges say is the price is by definition the right price.