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sharper
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Joined: June 8th, 2009, 1:25 pm

Interpolation between two matrices

May 16th, 2022, 12:20 pm

I would like to interpolate between two 8*8 matrices.  These are two transition matrices used for corporate bonds, with probabilities of moving between the ratings and to default.  
It is possible to use linear interpolation, but it has some distortion effects.  Is there a better way to do this?
 
Mercadian
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Joined: July 24th, 2020, 4:22 pm

Re: Interpolation between two matrices

May 16th, 2022, 1:41 pm

Hey Sharper,

Could you elaborate a bit more on your question? are the two matrices for two different dates? or for two different debtors? Also why are you trying to interpolate them, missing data?

M
 
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sharper
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Joined: June 8th, 2009, 1:25 pm

Re: Interpolation between two matrices

May 16th, 2022, 2:15 pm

It is a feature of Solvency II regulations for insurers that a full distribution is needed of each risk.  For defaults and downgrade risk for corporate bonds this means a transition matrix is needed at all percentile.  Some firms have used models like the Vasicek model (as outlined by Belkin) to do this.  But some firms have allocated specific percentiles to specific transition matrices; and an approach to interpolating between them....
 
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Alan
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Re: Interpolation between two matrices

May 16th, 2022, 6:05 pm

It is possible to use linear interpolation, but it has some distortion effects.  Is there a better way to do this?
Well, in principle the right way to proceed is via Bayesian updating: form a prior hypothesis, collect data, revise the probs, etc.