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2

You wrote: $$d[5] = (DJIR[5] - \mu) * Covariance$$ but you left out half of it (the inverse and the transposed vector on the right side). The correct formula is $$d[5] = (DJIR[5] - \mu)^2 / Var[DJIR]$$ The covariance "matrix" becomes the variance in a 1-dimensional case (in other words $x_i$ and $y_i$ are both equal to DJIR[i] in this case) and the "matrix ...

3

You can use refined methodologies but if you just need a rough estimation of liquidity, you can simply use an average of daily volume over N days. In practice, for equities, people tend to use N = 20 or 30. Once you have the average daily volume (say 100,000 shares), you compare it to your holding (say 50,000 shares) to determine the the size of your ...

1

I think one of the main liquidity measures is the one from Pastor and Stambaugh (2003). You can use it for both individual stocks or indexes. Just run the following intra-month regression with daily data: $r^e_{i,d+1,t} = \theta_{i,t}+\phi_{i,t}r_{i,d,t}+\gamma_{i,t}sign(r^e_{i,d,t}) \times v_{i,d,t}+\epsilon_{i,d+1,t}$. Where $r^e_{i,d+1,t}$ is the ...

1

I would consider Amihud (2002) as a good first approximation with that level of data.

0

Isn't the option's delta a close approximation for the probability the option will be in the money?

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