if it's for work, then read the discussion of Eq(30) here the point is that the ordinary estimate of covaraince matrix "as is" is not a robust tool to construct a portfolio. that's one reason why we have approaches like Black-Litterman

covariance loses information about the means. there's your answer

is this for fun or work?

Did you study measures in calculus curriculum? Did you study measure theoretic probability?

@AlanLui, good luck with that.

@AlanLui, you'll never get an answer to a question like that in finance. This is not a fundamental science like physics. If anything, there can be a ton of reasons why this model should not be the right model. It's simple and economists like to use it in studies where the exact evolution of rates is not so important. It captures mean reverting characteristic.

The model itself is known as Ornstein Uhlenbeck process in physics. Did you read Vasicek paper?

The prices are usually correlated, the returns may not. That's why it's almost pointless to look at ACF of price series. Pull up efficient market hypothesis and convince yourself that it has nothing to do with the price chart of yours

In our feed if the option is thinly traded, you get the stale prices for options, i.e. prices from trades days ago. When you have far OTM options, the underlying often moves enough to make the option price impossible, you can't calculate IV. Without IV you can't calculate greeks

@zer0hedge, sorry, I misunderstood your question. The abs of return is an estimator of the volatility, that's the reason why you see autocorrelation, see here

Not trying to be negative here, but I'm afraid the topic is too broad. For instance, Dodd-Frank itself is a vast area with a ton of discrete SRs from FRB and OCC, which target various areas. Then you have FINRA, SEC, PCAOB etc. It's a beast. In the banks we have special departments (compliance and legal) whose sole purpose is to track what's relevant to a given institution