The first, in a well-known paper by Fengler: http://www.javaquant.net/papers/Fengler.pdf , see proposition 2.1 on page 11, and the second in an equally well-known paper by Gatheral: https://arxiv.org/pdf/1204.0646.pdf , see lemma 2.1 on page 3.

It seems to me though that the proof given in Fengler (which is actually due to Reiner) is more general than the Gatheral proof, since the latter explicitly assumes martingale property, whereas the former relies purely on no-arbitrage arguments and so the underlying can also be a local martingale? Anyone thoughts on this / (dis) agree with my conclusion?

Statistics: Posted by frolloos — September 21st, 2017, 6:50 pm

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I'm not behind a computer right now, but you can validate your result yourself if you can generate random samples of the distribution. First sample from the 1 day distribution, then sum n random samples to get b-day return samples, and then compare distributions.

Statistics: Posted by outrun — September 20th, 2017, 12:55 pm

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Statistics: Posted by mcbison — September 20th, 2017, 9:54 am

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t=2

alpha1=pd.alpha;

beta1=(t*(pd.beta*abs(pd.gam).^pd.alpha))/((abs(pd.gam.^pd.alpha))*t);

gam1=t*((abs(pd.gam.^pd.alpha)).^(1/pd.alpha));

delta1=t*pd.delta;

pd1=makedist('Stable','alpha',alpha1,'beta',beta1,'gam',gam1,'delta',delta1)

y_scaling=pdf(pd1,x_value)

plot(x_value,y_scaling,'Color','g','LineWidth',2)

Statistics: Posted by mcbison — September 20th, 2017, 8:37 am

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Statistics: Posted by mcbison — September 20th, 2017, 8:27 am

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alpha1=pd.alpha;

beta1=t*(pd.beta*abs(pd.gam).^pd.alpha);

gam1=((abs(pd.gam.^pd.alpha))*t).^1/pd.alpha;

delta1=t*pd.delta;

pd1=makedist('Stable','alpha',alpha1,'beta',beta1,'gam',gam1,'delta',delta1)

y_scaling=pdf(pd1,x_value)

plot(x_value,y_scaling,'Color','g','LineWidth',2)

but it is wrong I don't know why

Statistics: Posted by mcbison — September 20th, 2017, 8:22 am

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So from convolution: u2=ut ?

c?b? and alpha? respect the time? I would be grateful if you can help me for a moment, I'm not very familiar with convolution ( I know what it is but I'm not a fine mathematican).

Can you help me?

So I have matlab code to calculate 1 period alphastable stop loss and I have to implement multiperiod

Statistics: Posted by mcbison — September 20th, 2017, 7:33 am

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Even though these distributions have a very nice property that sums of multi-day returns stay in the same family of distributions, and that the distributions allows for non-linear variance scaling across time-scales, these distributions have nasty properties, in particular infinite variance.

If you're looking for Hurst and Fractal stuff then it might be better to start with Fractal Brownian Motion: https://en.wikipedia.org/wiki/Fractional_Brownian_motion

Statistics: Posted by outrun — September 19th, 2017, 10:16 pm

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How the 4 parameters are proportional to the time?

thanks a lots

Statistics: Posted by mcbison — September 19th, 2017, 8:47 pm

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This doesn't answer your question and is not directly related but it might be something to keep in mind:

https://www.bloomberg.com/news/articles ... amond-debt

We are in a country with the best reputation for Mining and I don't see diamonds exceeding 20% of our portfolio.

Statistics: Posted by Tedypendah — September 10th, 2017, 11:53 pm

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Statistics: Posted by Amb — September 7th, 2017, 9:50 am

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Suppose I have a portfolio of investments with a finite number of outcomes.

1% of the time, I lose everything.

3% of the time, I lose exactly 40% of my investment.

6% of the time, I lose exactly 25%

10% of the time, I lose exactly 10%

80% of the time, I gain exactly 15%

For this portfolio, the most you will lose at the 95% level is 25% of your investment.

If my risk limit is 10million BWP, then I would invest 40million BWP.

the most you will lose at the 95% level is 25% of your investment, and 25% of 40million is 10million, your risk limit

Statistics: Posted by ppauper — September 6th, 2017, 8:09 am

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- Line of business (& have correlations between Early Stage & Growth Capital)
- Commodities (& have correlations between Diamond, Coal, Quarries, Salt etc)
- The VAR is just multiplying correlation matrices with nominal values

Statistics: Posted by Tedypendah — September 5th, 2017, 11:36 pm

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Do you have some ideas about how to come up with a loss distribution? What losses can you expect with what probability?

Statistics: Posted by outrun — September 5th, 2017, 11:15 pm

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