One of the big topics I see running through my current and planned research is the idea of prices as essentially emergent phenomena that have a less precise existence in a lot of contexts than we often pretend. Transactions have precise prices; offers to transact have precise prices. Assets with centralized, fairly liquid markets have fairly precise prices; a firm offer to sell at a particular price more or less refutes any price higher than it, and a firm offer to buy (a bid) at a particular price more or less refutes any lower price, so two such offers close to each other, especially with large sizes, pretty well pin down the market price of even a moderately sized trade. Smaller cap stocks often have only loosely defined prices. Real estate generally has something an appraiser pulled out of his
Corporate bonds don't have liquid markets, or centralized ones (even in the sense that stocks do under Reg NMS). Corporate bonds are an important asset class, and there are price indices that attempt to give a sense of whether the prices are going up or down and by how much. There are various ways of doing this, and they aren't uniformly terrible; many of these indices are in some reasonable sense more or less correct, to about the degree that such a thing can be correct. There are some contexts in which they run into the problem that they're weighted sums of numbers that don't actually exist, though.
Exchange-traded funds (ETFs) are more or less, as the name has it, exchange-traded shares of mutual funds. Unlike closed-ended funds, the number of shares is variable, and essentially determined by the market; unlike open-ended funds, most of the activity consists of buyers buying existing shares from sellers. Unlike either, at least in their most common configuration, their holdings are publicly known and basically static; a share of the fund may represent .08 shares of one stock, .03 shares of another, and so on. The ETF has a sponsor, and a redemption size; if the redemption size is 75,000 shares, and you go to the sponsor with 75,000 shares of the fund, the sponsor will exchange them for 6,000 shares of the first stock, 2,250 of the second, and so on; conversely, if you take those underlying stocks to the sponsor you can receive 75,000 shares of the fund in their place. Even if all the stocks involved have very liquid markets, you can occasionally have a small difference between the price at which the ETF is trading and the weighted sums of the prices of the underlying stocks, but if the difference gets at all appreciable big institutional investors will start buying whichever is cheap and selling whichever is expensive and the sponsor will end up creating or redeeming shares. Because everyone knows this is likely to happen, it doesn't need to happen very often; if traders believe that a big purchase or sale of ETF shares is a short-term event, they may sell or buy, partially hedging with a subset of the underlying basket, in the expectation that the prices will return to parity. (If you google something like "stabilizing speculation gold points" you can probably find a description of how this worked under the gold standard when the "sponsor" was a central bank and gold was being exchanged for currency.)
Once in a while ETFs need to change their holdings; an ETF that tracks the S&P 500 stock index adjusts its holdings when the constituents of the index change. In the case of bond funds in particular, bonds will mature every now and then, and rather than just pay out the cash some new issue is typically added to the fund and the fund continues its existence. There are bond ETFs, though, and they work in ways that are mostly unsurprising. In the case of corporate bond ETFs in particular, though, the underlying securities often lack liquid markets, and often only really trade once or twice a week; the ETFs are often a lot more liquid than many of the underlying issues, which is big part of the value that the ETFs add.
Curiously, though, there are some people who are troubled by this, particularly where the ETF is attempting to track a bond index. Even if the ETF itself is liquid (and thus has a fairly well-defined price), the price of the ETF may fail to track the index. This is a failure of the index, not the ETF. Indeed, one great value the ETF is adding in this scenario is that it is giving a better measure of the index; a lot of "incorrect" values for the basket are being "refuted", including possibly one calculated by the index methodology, which most likely (in this scenario) is leaning too heavily on stale prices — too much pretense that the "price" of a bond that hasn't traded since Tuesday is the price at which it traded on Tuesday.
I would propose, in fact, that where an index (basket) might accommodate a more liquid market than many of its constituents, that the best way to define the index may be as the "price" of an associated ETF. There are ways of tracking repeated sales (the Case-Shiller index does a pretty good job of this), but most of the time, if there's a clear conflict between the price of the ETF and the calculated value of the index, I'm better that the price of the ETF is more current and more correct.