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2

When $x_i$ is the return of the $i$th asset, the returns of portfolio $\vec{w}$ are $\sum_i w_i x_i$. The covariance of the returns of two portfolios, $\vec{w}$ and $\vec{v}$ are then $$\sum_i \sum_j w_i v_j \operatorname{cov}\left(x_i, x_j\right).$$ Now note that $\Sigma_{i,j} = \operatorname{cov}\left(x_i,x_j\right)$. The rest is confirming that this ...

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I agree with @Kermittfrog's comment, that this only works if you do not impose any budget constraint (in the sense that your weights sum up to one). Other than that, I am sorry that I can not precisely answer your question where it was first derived (tbh: I am not even sure if it was explicity derived at all somewhere because it simply follows from the very ...

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Pearson 2 skewness, which compares mean and median, lying between $-3$ and $3$ while being zero for symmetric distributions, was introduced by Yule, G. U. and Kendall, M. G. (1950), An Introduction to the Theory of Statistics, 3rd edition, Harper Publishing Company, 162-163.

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It is covered very nicely in Iain Clark's Foreign Exchange Option Pricing, A Practitioner’s Guide (pages 98-104). The book also contains references to the relevant literature including Feller's original paper.

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I believe your SDE has an unintended error. It should be: $$dr_t = a \cdot (b - r_t) \cdot dt + \sigma \cdot \sqrt{r_t} \cdot dB_t.$$ On the other hand, the Feller condition is discussed and explained in Section 10.2.1.2 (pg. 432) of the Andersen and Piterbarg book: Interest Rate Modeling. Hope it helps!

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References https://www.bis.org/publ/bcbs265.pdf This one is directly used by banks for programs such as FRTB. https://assets.kpmg/content/dam/kpmg/xx/pdf/2018/10/frtb-white-paper-july-2018.pdf. This one describes it from a P&L variance ratio point of view. https://en.wikipedia.org/wiki/PnL_Explained. Basic summary of P&L attribution. Summary The ...

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I'm not aware of any great reference. However Peter Nash Effective product control: controlling for trading desks. Wiley (2018) chapter 10 Review of Mark-to-Market P&L is a good start. I wrote some notes here that I hope may help. You should have risk-theoretical P&L (RTPL - Taylor sereis approximation of the P&L) for all positions. For the ...

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An Evaluation of Change Point Detection Algorithms might be of use.

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"what value would there be in clustering the individual sample observations within that stock's historical prices series, or its return series? is univariate clustering done in finance?" Seen clustering used for regime identification in the time series of returns for a single asset.

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This is seen as a bit of a niche field, which is likely why there are not so many books and these issues are not covered in standard econometrics texts. Options pricing models are usually fitted to options data rather than estimated econometrically from historical data. For statistical models, it is often more convenient to start from a discrete model as the ...

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