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Modelli per il Calcolo del Value at Risk

Modelli per il Calcolo del Value at Risk

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Σ<br />

M<strong>at</strong>rice Varianze – Covarianze<br />

La m<strong>at</strong>rice di covarianze dei rendimenti è<br />

=<br />

⎡<br />

⎢<br />

⎢<br />

⎢⎣<br />

β<br />

1<br />

...<br />

β<br />

n<br />

⎤<br />

⎥<br />

⎥<br />

⎥⎦<br />

[ β ... β ]<br />

1<br />

Σ<br />

Slides AB <strong>Mo<strong>del</strong>li</strong> <strong>per</strong> <strong>il</strong> calcolo <strong>del</strong> <strong>Value</strong> <strong>at</strong> <strong>Risk</strong><br />

=<br />

ββ<br />

n<br />

σ<br />

′ σ<br />

2<br />

2<br />

m<br />

m +<br />

2n+1 parametri da stimare: n valori <strong>del</strong> vettore β ;<br />

n elementi <strong>del</strong>la m<strong>at</strong>rice D ; la varianza <strong>del</strong>l’indice<br />

+<br />

⎡<br />

⎢<br />

⎢<br />

⎢<br />

⎣<br />

D<br />

σ<br />

2<br />

1<br />

...<br />

0<br />

...<br />

...<br />

...<br />

0<br />

...<br />

σ<br />

2<br />

n<br />

⎤<br />

⎥<br />

⎥<br />

⎥<br />

⎦<br />

42

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