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easy
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Joined: July 14th, 2002, 3:00 am

Yield curve evolution via modelling zero rates?

October 10th, 2012, 9:02 am

I am looking at various vendor risk engine engines and quite a few evolve zero rates as log ornstein-uhlenbeck processes. I haven't seen any academic papers on this, but some simualtion and a bit of analysis shows that the zeroes must be highly correlated to give reasonable forward rates. Using historical correlations and vols doesn't give goods results, ie negative forwards or very large forward rates. This make sense as the forwards are derivtaives so we want the zeroes to be smooth, but the historical vols and correlations don't support this.Has anyone ever tried modelling a yield curve by evolving zero rates?
 
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wickedwit
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Yield curve evolution via modelling zero rates?

October 14th, 2012, 3:24 pm

Why would you want to evolve the zero curve instead of the cash curve? I would think that simulating the cash curve would lead to more reasonable results and thus reasonable and intuitive forwards and zeros. Why not just simulate the cash curve and bootstrap for your forwards and zeros?
 
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easy
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Yield curve evolution via modelling zero rates?

October 25th, 2012, 8:39 pm

The vendor system has log normal mean reverting and normal mean reverting as default models for FX and IR. I haven't seen this discussed anywhere else, so was wondering if other people with vendor systems have encountered this problem.
 
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amike
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Joined: October 21st, 2005, 12:57 am

Yield curve evolution via modelling zero rates?

October 25th, 2012, 9:43 pm

I think this is usually motivated by standardization -- fit the market data every day to find a set of fixed term zero rates so that you are calibrating your process to a consistent historical data set. This is not always a good idea of course... Also I think some of these vendors are hopelessly stuck in the 80s.I ran into the same problem with forecasting par swap rates with OU processes -- be careful with the mean reversion parameters, they can have a large impact on this issue and typically cannot be consistently estimated using historical return data: the values are almost always statistically insignificant (mean reversion typically over years that you are trying to estimate using daily returns). A bit of creativity with setting mean reversion seemed to make this problem largely go away (i.e., there weren't 'too many' obviously ridiculous scenarios).Try doing a best fit to market implied--that also seemed to keep the problem at bay...
 
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easy
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Yield curve evolution via modelling zero rates?

October 25th, 2012, 9:48 pm

We found that the historical correlations and vols for USD zeroes were "discontinuous" particularly in the short end, which caused a lot of grief. Thanks for the market implied tip. I will have a look at that. If this was an internal build we would have done it differently, but expected that the standard models would give reaosnable results. Unfortunately that is not the case and, as you suggets, we have had to be creative to get sensible results.