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The motivation of the Cornish-Fisher expansion is to approximate quantiles when the data is not normally distributed. It may help to think about parameters of a probability distribution and the resulting variance of the probability distribution. For instance, a normal distribution has two parameters, a location and a scale. It turns out that the maximum ...

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We know the formula to price a call option in the Black-Scholes-Merton model: $$C=S_0\Phi(d_1)-e^{rt}K\Phi(d_2)$$ with $d_1=\frac{\log\frac{S_0}{K}-T(r+\frac{\sigma^2}{2})}{\sigma\sqrt T}$ and $d_2=d_1-\sigma\sqrt T$, assuming the underlying stock pays no dividends. The option delta is given by: $$\Delta:=\frac{\partial C}{\partial S}=\Phi(d_1)$$ Note that ...

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Consider you have positions in $N$ assets, with market values $S$, and that the daily PnL is acquired via multiplying the daily returns vector, which is a random vector with some unknown joint probability distribution. $$p = S^T R$$ You are interested in variance of $p$ for constant $S$: $$Var(p) = E[(p-E[p])^2] = E[(S^TR - E[S^TR])^2]$$  Var(p) = E[(p-...

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I googled and found https://github.com/TommasoBelluzzo/BaselTools . It says: BaselOP The tool can be run by executing the BaselOP.m script. The underlying calculations are based on the SMA model defined within the BCBS 356. The application offers the opportunity to compare the SMA capital requirements with those produced by the obsolete Basel II approaches ...

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