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Market Risk VaR takes one year of history. Thus you wouldn't look 5-10 years of history. If you are using CDS prices only for pricing CDSs you don't need to, but if you have another model that takes CDS prices and links them to bonds, yes You don't need PCA. You can take quotes on CDSs closest to each term node, but you need to roll them to adjust for ...

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The first part has already been answer by @Uditg_ucla, so I am only providing answer of your 2nd part. Rewriting your SDE in more sophisticated way: $$dS=k(b-S)dt+\sigma S dz$$ You want SDE for $S^2$. Using Taylor series, it can be written as: $$df(S)=f'(S)dS + \frac{1}{2!}f''(S)(dS)^2+\cdots$$ $$df(S)=2SdS+(dS)^2$$ df(S)=2S[k(b-S)dt+\sigma S ...

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Compare these two links: https://en.wikipedia.org/wiki/Distortion_risk_measure https://en.wikipedia.org/wiki/Spectral_risk_measure Then these risk measures are only different by their assumptions on the distortion function: $\tilde{g}$ is the dual distortion function $\tilde{g}(u) = 1 - g(1-u)$ with $g: [0,1] \to [0,1]$. $\phi$ is non-negative, ...

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