FIRM SIZE, INTANGIBLE ASSETS & BID-ASK PRICE.... these data should be accessible with any database portals. Select you stock exchange that you want to work with, the website of that exchange should be accessible on free access basis to its historical data. Firm size and assets (tangible & intangible) are generally reported in their SEC annual & quarterly filing. Ask & bid price should be available through historical data menu on the website either in excel format or html.

Some relevant articles on measuring and modeling information asymmetry in firms are attached. Cheers. 

If the M&A transaction happened in the past it may well be that data on the target no long resides in current databases.  So if you were taking a historic perspective you would need to access historic data before the M&A transaction took place.  London Business School used to have a library dedicated to historic business data - all in hard copy I'm afraid.  It may be that other business school libraries can assist. 

As to other informational asymmetries, the data you suggest is typically publicly available during the M&A process.  I would also seek the target company's risk profile and the extent of insurance coverage.  Although many risks can be insured, those policies will have upper limits; and many types of risk (eg market risk) cannot be insured.  Risk is likely to be an informational asymmetry in which case the acquirer will need to make whatever inquiries they can and an informed guess as to where the key risk exposures lie. 

Thank you very much for the answers, much appreciated !

Dear Wong

In my opinion, in the case of a M&A Deal, it is more difficult in measuring the Information Asymmetry, so you should be careful in working on this field

I suggest you consider the "bid-ask spread" and look for more information on the attached file below

I hope that it is useful for you

Bests

Taking the book value of a firm (B) and comparing it to the market/stock price (P) of a firm, the relative disparities between them may be indications of information asymmetry between the firm's internal stakeholders and its external stakeholders. For instance if we  construct the book-to-market ratio: B/P, and the value of this ratio exceeds or is less than 1, then information asymmetry exists. Information asymmetry is to be expected what bothers people are the risks associated with information asymmetry.Under suitable assumptions this may signal heightened risks or diminished risks as well. For instance, the degree of which the value of the ratio was coincidental to the M&A deal finalization date.

Rather crudely B/P>1, is indicative of relatively high tangible assets;and B/P