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The paper "Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density Estimation" by Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2018) gives a large number of CVAR analytical formula with full proof. Most of them can also be found on the Expected shortfall (aka CVAR) Wikipedia page.


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I assume that you calculate ECL in the context of IFRS9 -correct? market practice often follows the following appraoch: estimate a TTC PD/LGD (TTC = through the cycle). This corresponds to your lifetime estimate (e.g. one marginal PD value for each year of the life of your exposure) in the average of the economic cycle. But for IFRS9 provisioning you have ...


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You are building a model - the question you are asking is a trade off between accuracy and complexity. If the accuracy only improves in a minor capacity and the extension is considered complex you can ask the question "is it really necessary"? If the accuracy greatly improves then whether the extension is considered complex or not I suspect that for ...


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Here are a couple of the flaws I see: Your measures of correlation/cointegration are likely to depend on the period chosen for the analysis. These can be quite variable, and your hedge portfolio may not perform as well as you expect out of sample. Given that, your hedge portfolio is likely to place an emphasis on the stocks that appear closest to the ...


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Hi: Assuming you can buy a risk model for the EuroStoxx 50 or estimate one, then this implies that you have all the exposures (risk and industry) for the stocks in that index. Then, once you have that, you can construct an optimization that says minimize risk and industry factor differences between portfolio and alcoholic beverage company subject to A) ...


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This is (to a degree) how fixed income is still rated, particularly in CLOs and MBS/CMO. The risk of default on the ABS is mitigated by overcollateralizing the senior tranches and the joint probability of default of each underlying asset. The risk premium in ABS pricing is due to the possibility of systematic risk, as opposed to idiosyncratic risk (which has ...


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You could decompose the portfolio dv01 by buckets (corresponding to the available futures) and hedge each bucket with the appropriate number of contracts.


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