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I assume that you calculate ECL in the context of IFRS9 -correct? market practice often follows the following approach: estimate a TTC PD/LGD (TTC = through the cycle). This corresponds to your lifet …

There are several aspects: The holding period that you want to measure: Usually, you want to calculate VaR for a specified holding period. For USCITS funds it is e.g. 20 days for bank pillar 2 regulat …

Yes, investors want to earn more than risk free but do they always get it? Or does the risk premium just fill the gap - sometimes positive sometimes negative? … Sometimes stocks are just falling and there is risk and no premium. What do you think? …

Do you have multiple observations of this relation? If so then you could perform linear regression and perform all the regression diagnostics.

I don't know whether this question is in order here. I do a bit of teaching and I am preparing my own notes but I thought that his should not be necessary. In which book/pdf on the web can we find a …

The next question is what the aim of your risk measures is. … portfolio B or my portfolio is riskier or less risky if I add/remove a tiny position in stock S then I would say: Variance is (of course) as fine as standard deviation (volatility); a Gaussian Value-at-Risk …

Translation invariance of a risk measure $\rho$ is defined as $$ \rho(X+k) = \rho(X)-k, $$ where $X$ is a random variable such that $\rho(X)$ exists and $k$ is a constant. … The meaning is that if I add an amount $k$ to my risky positions then the risk is reduced by this amount. …

I would like to model OTM Swaptions. I can use some implementation of the Bachelier model (not B76 due to negative rates) and implied volatilities from Bloomberg. For 10Y X 10Y (10 years option matur …

I assume that risk it measured here in volatility. … Thus we should invest all our wealth in stock A and the minimal risk is 25%. If the volatolity of B were smaller it could reduce risk to invest in B. …

You can do 2 things: incremental risk: Calculate the volatility with the asset and with the asset replaced by cash. … The difference gives you the (non-linear) incremental risk contribution of the asset. …

Let us ignore the riskless rate for simplicity of the presentation. If you have (historical or simulated) return series $r_i$ for the portfolio and $r_i^M$ for the market, then the beta is the OLS reg …

The VaR of level $\alpha$ a loss random variable (the bigger the worse) is the quantity $q$ such that the loss is bigger with probability $1-\alpha$. Thus we need a $q$ such that $$ P[L>q] = 1-\alp …

We define a convex risk measure as $$ \rho( \lambda X_1 + (1-\lambda) X_2) \le \lambda \rho( X_1 ) + (1-\lambda) \rho(X_2), $$ for $\lambda \in(0,1) $. … Thus a coherent risk measure is convex. The reverse is not true in general. …

I though about this one more time: method of moments means that you do the following: calculate some statistics (i.e. the moments) on the sample express the moments of the distribution that you wan …

For the formulas for the momemts of $S$ look here or google "moments in the collective risk model". …