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Alkmene
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Posts: 301
Joined: January 18th, 2007, 10:19 pm

Var-Covar matrix simple

September 23rd, 2009, 9:26 pm

Guys,thanks for any help on this; I guess it is covered somehow by all the questions and answers on this topic discussed before but I can't filter the necessary bits to understand the following.If I am trying to model some kind of set of RVs (call it a basket of sorts) I need to consider the case where the Cov/Corrs are non zero.Suppose I can infer the expected value of the Volatility from some market (implied vols from traded options) but there is no market for the correlation not even implied, how do I mix historical correlation and implied vols to get a consistent Var/Covar matrix? Anything I need to look out for? E.g., could the situation arise where CoVar(x,y)/((Var(x)*Var(y))^.5 > or < +1 or -1 when I mix those implied with historical values?Thanks,Alk
 
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PatrickM
Posts: 27
Joined: August 8th, 2002, 1:40 pm

Var-Covar matrix simple

October 2nd, 2009, 1:51 pm

You can't have negative eigenvalues. Do the eigenvalue matrix decomposition, if you can, and then substitute zeros for all the negative eigenvalues, then multiply back together to get a usable covariance matrix.
 
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ACD
Posts: 107
Joined: April 19th, 2004, 8:09 am

Var-Covar matrix simple

October 2nd, 2009, 2:07 pm

This paper may be useful tooThe most general methodology to create a valid correlation matrix for risk management and option pricing purposes
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