Why do we take market prices as the prices to be estimated and predicted? The common answer is efficient markets hypothesis as in "Market agents do their best effort given their information set, therefore market prices are optimal." Is there another way?
Edit: I should add that it is the academic way of doing this. If you are to publish a paper you show how well your model represents the market compared to other models. See an example
Suppose I have a nice option pricing model (say Model A) to estimate some option contracts' fair prices. I use this model to estimate some of the contracts existing in the market. Let's denote the set of the price estimates as "Estimate Set A".
And let's say there is another option pricing model (say Model A) doing the same thing and get some estimates as "Estimate Set B".
And then we have the market prices since those are exchange traded options. And let's call them, well, "Market Prices".
I would like to know whether model A or model B is a 'better' option pricing model.
From what I have seen on numerous academic studies, the convention is to use an error function like root mean squared error (RMSE) and sometimes relative pricing error or some other derivation and take the Market Prices set to measure the error from. To illustrate let's say there are 4 contracts Estimate set A consists of (1, 2, 3, 4) and estimate set B consist of (4, 1, 3, 2) and market prices are (2, 3, 2, 3).
RMSE of A is sqrt((1-2)^2+(2-3)^2+(3-2)^2+(4-3)^2) = 2 RMSE of B is sqrt((4-2)^2+(1-3)^2+(3-2)^2+(2-3)^2) = sqrt(10) ~ 3.16
Conclusion: A is better than B (of course it is slightly more complicated)
The only rationale I can find from the literature behind this logic is the assumption that comes from efficient markets hypothesis.
All that is required by the EMH is that investors' reactions be random and follow a normal distribution pattern so that the net effect on market prices cannot be reliably exploited to make an abnormal profit, especially when considering transaction costs (including commissions and spreads). Thus, any one person can be wrong about the market—indeed, everyone can be—but the market as a whole is always right.
Option pricing performance convention is built right atop of this hypothesis. The problem is the implicit assumption of the market price optimality. If the market prices are optimal then there is no way a model can be used as a trading strategy.
Suppose your model estimate the price of the contract as 1.5 (say dollars) and the market price of the contract is 1.2. If you gauged your model with the market prices you should accept you are off 0.3$. So why bother with a model, even more why bother with trading?
Is there any other way?