As I keep thinking about Libor fixing (see my post last week on this), I have realized that the word price is used in many ways to mean many things not all of which deserve to be called a price:

An actual traded price
This is the simplest and perhaps most unambiguous definition of a price. The only problem with this notion is due to illiquidity. If the asset is highly illiquid, there may be no recent traded price. More commonly and more importantly, the traded price is subject to the bid-ask bounce – a trade initiated by the seller executes at the bid price while a buyer initiated trade executes at the ask price. If the stock is traded frequently enough and the bid-ask spread is small in relation to the desired level of accuracy, the traded price is a clean and transparent definition of price.
The mid price
Even if the stock is modestly illiquid, there is often an ask price and a bid price in the order book and the average of these is a reasonable approximation to the true price. It is probably better however to use the entire bid-ask interval instead of just the mid price to communicate the range of uncertainty about the true price. Moreover, the bid and ask are valid only for small transaction sizes. It may be better to use the full information in the order book to do an impact cost calculation and present the bid and ask for a more reasonable order size.
An average of traded prices
Quite often closing prices on an exchange are determined as averages of prices during the last few minutes of trading – though in some cases, “few” gets stretched to quite a long period. This averages out the bid-ask bounce and is a tolerable approximation if the volatility of the “true” price during the averaging period is small in relation to the impact cost of a reasonable trade. Sometimes, the averaging is designed to deal with attempts to manipulate the closing price and then it may be reasonable in the above comparison to use the impact cost of the expected trade size of a potential market manipulator which may be significantly larger than typical trade sizes. An alternative to averaging is to use a call auction to determine the closing price.
Polled or indicative prices
Libor and the well known US Constant Maturity Treasury (CMT) fall in this category. The attempt here is to average over market participants’ quotes about what they believe is the true price. The difference between polled prices and traded prices is like the difference between an opinion poll and an actual election. I think it is a mistake to base large derivative markets on “opinion polls”.
Model prices
In the absence of traded prices, it is common to use a pricing model to estimate prices. Of course, there are several shades of grey here: accountants talk about Level One, Level Two and Level Three assets to capture some of the greyness. Outside of finance, hedonic estimates of the price of real goods are also model prices. For an even more extreme case, one could consider a surveyor’s real estate valuation opinion as a model price where the model is less precisely articulated. At the opposite end in terms of formalization of models, the equilibrium prices derived out of general equilibrium models are also model prices with the added twist that in many of these models, the no trade theorem is actually in force and the model price is an estimate of the price at which nobody wishes to trade. My own view on this is that model prices are valuation opinions and not prices.

Where does that leave us? I think that for liquid assets, actual traded prices (perhaps determined by a call auction) are the best way to define the price. For illiquid assets, it is best to recognize that there is no unique price and to use a price interval as the best way to communicate the range of uncertainty involved. I do not understand why physicists are quite happy to say that the gravitational constant in appropriate SI units is 6.67384 ± 0.00080, but in finance and economics we are unwilling to say that the price of an asset is 103.23 ± 0.65.

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