Hi,
if I calibrate Alpha-Stable distribution on daily data or intraday data, how can scaling it in weekly o annual distribution?
How the 4 parameters are proportional to the time?
thanks a lots
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Re: Time scaling of alpha-stable process
If you assume your 1-day return is Alpha-Stable distributed, then the parameters of your 2-day return distribution is given by this "convolution" property:
https://en.wikipedia.org/wiki/Stable_di ... Properties
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/Fractiona ... ian_motion
https://en.wikipedia.org/wiki/Stable_di ... Properties
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/Fractiona ... ian_motion
Re: Time scaling of alpha-stable process
I use alpha-stable only to calibrate my stop loss as ocam razor for trading. My stop loss distribution is the difference between alphastablepdf - alphastablepdf (x-2*K,p) where K=log(H/S) H stop loss S asset value.
But I want to calculate multiperiod stop loss, so I have to scaling distribution.
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
But I want to calculate multiperiod stop loss, so I have to scaling distribution.
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
Re: Time scaling of alpha-stable process
%convolution for time scaling
t=10
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
t=10
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
Re: Time scaling of alpha-stable process
this is the result of my code to scaling of alpha stable
It is wrong
It is wrong
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- alpha stable scaling
Re: Time scaling of alpha-stable process
ok I find the mistake
I think this is correct
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)
I think this is correct
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)
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Re: Time scaling of alpha-stable process
My result for a multiperiod stoploss probability with alphastable distributuion
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Re: Time scaling of alpha-stable process
Convolution (of probability densities) is just a fancy name for saying the distribution of the sum of returns, like the sum of two consecutive days.
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.
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.