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Conversion to a butterfly can mitigate or even eliminate all risk taken by opening a initial debit spread or long option position. This is possible only if the underlying moved in your favor after your initial position is open. To convert to a butterfly you simply sell and buy enough options (for a credit) that together with your initial position forms a ...


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A risk measure $\rho$ applied to time series $X \in \mathbb{R^n}$ yields $Y \in \mathbb{R} $. i.e. $\rho: \mathbb{R^n} \rightarrow \mathbb{R}$ As for implementation (using R), see here. A look at the formulas for VAR and ES (which is exactly the same as CVAR) should clear up any confusion.


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For starters, one can argue they provide a better fit to the distribution of asset returns than a Normal distribution simply because stable distributions allow for more degrees of freedom. I had a discussion with a very well-known financial mathematician on the subject of using stable distributions as the return process for derivatives pricing, and his ...


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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 want to fit in terms of the parameters of this distribution solve the resulting system of equations. If you estimate $E[S^n]$ by averaging the ...


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as you post 3 questions on this topic and after reading them: this is homerwork/study material- right? So for comparing Fast Fourier, MC and Panjer there are tons of publications out there. For the formulas for the momemts of $S$ look here or google "moments in the collective risk model". You should notice that: If you know the distribution of $N$ and $X$ ...


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If the bond's DV01 is 0.05, then the DV01 of 1000 of this bond will be $0.05\times 1000 = 50$. By contrast, if the modified or effective duration of the bond is 0.05, then the modified duration of 1000 of this bond is still 0.05.


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You can do the following: For each $i$ in $1$ to number of Mont-Carlo runs $K$ simulate the number of losses $N_i$ simulate $N_i$ many loss-sizes $X_{i,1},\ldots,X_{i,N_i}$ calculate $L_i = \sum_{j=1}^{N_i} X_{i,j}$ Doing this you get a sample of losses $L_1,\ldots,L_K$ and you can do all sorts of hisograms, density fits, VaR, ES calculations on it. ...


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if you have $p=0.5$ For example: $U(w)=ln(2w)$ why is that? relative risk aversion is given by $$RRA=\frac{-wU''(w)}{U('w)}=\frac{-w*(-1/4w^2)}{1/2w}=0.5$$ Now you can apply your formula. take for example: $x= 10000$ and $\pi=0.5=1-\pi.$ then expected utility is equal to $EU(x,w)=0.5*ln(2*(w+x))+0.5*ln(2*(w-x))=0.5ln(220000)+0.5ln(180000)$ you want to ...



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