Let me give you three or four of my papers. It will solve your problem. The answer "why" is simply too long to answer here. The basis of my papers is that returns are not data. Prices are data and returns are a transformation of that data. It follows then that you cannot make assumptions about the distributions of returns, but you can either derive the distribution of prices or you could make assumptions about the distributions of prices. You could actually show that it is mathematically impossible for equity prices to be either normally or lognormally distributed. It isn't possible as it would create a mathematical contradiction in an option pricing model.
It turns out that you can derive the distribution of prices by using the rules that derive the price structures and the error terms. It is also well understood in statistics how to do the transformations necessary to determine the distribution of returns for an asset class. So, for example, under Markowitz's assumption, returns on investing must be the ratio of two, independent, normal distributions centered on (0,0) in the error space. On the other hand, if you were buying and selling assets at Sotheby's, such as art, then you will encounter the ratio of two Gumbel distributions. The rules determine the distributions. Other issues, such as the budget constraint, the cost of liquidity, merger and bankruptcy risk are part of the rules and so in part determine the final distribution.
This in turn determines the rules of econometrics, which in turn determines the rules for pricing options. I also did a population test as a partial verification.
The papers at the page https://papers.ssrn.com/sol3/cf_dev/AbsByAuth.cfm?per_id=1541471 will explain why the papers see systematic mispricing. I am working with a measure theorist to extend the laws of stochastic calculus to include this situation and would like to have a fundamental extension of the rules of calculus prepared by Spring break. I have also started a paper on subjectively optimal portfolios, but I am teaching six classes so it won't be finished before summer. Just a warning, I put rough drafts out there, so the calculus paper, when it first comes out, could have poor language or be missing a boundary condition or something like that.
Please feel free to send any criticisms.
EDIT You can tell something is mispriced in two ways. First, you can do a correlation study to see if option prices are correlated with actual outcomes. Second, you can use the method of inverse probability, as is done in one of the papers referenced, to test the assumptions directly.
Informally, the findings excluded Ito calculus models from use. Because an inverse method was used, a prior probability for mean-variance finance was used, giving it 999,999:1 odds of being the true model or something like it, over the alternative that no variance existed, and it was still falsified despite prior bias.
If you have not used Bayesian or inverse methods, http://www.seaturtle.org/mtn/archives/mtn122/mtn122p1.shtml?nocount provides an informal account. A good set of youtube videos of a grad course on them are at http://www.youtube.com/user/opinionatedlessons/videos?view=0&flow=list&sort=da