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th14
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Posts: 1
Joined: November 9th, 2017, 7:25 pm

Simulating MBS prices from durations

November 9th, 2017, 7:43 pm

I can pull historical MBS prices from TradeWeb and use a cholesky decomposition matrix to simulate correlated random prices.

However, I am interested in doing this using a forward looking metric: duration off Bloomberg.

Let's say I have two assets, [x] with a 2 duration and [y] with a 1 duration.

This implied the formula for line between these two securities' price movements is [x] = 2/1 [y] ...  which implies the beta is 2.  For the inverse, the beta would be 1.

Where I am getting hung up is that the durations seem to imply a perfect correlation between the two assets.  beta_xy = 1 / beta_yx.  This situation only holds if the correlation is exactly 1.

So what's the preferred approach?  Even if I use a whole loan model with a fancy yield curve simulator, I'm still modeling using the same underlier...  The resulting price strips will appear "over correlated" and I miss out on the supply/demand mechanics that could account for variances "within" the durations.

I sort of feel like I'm missing something...
 
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ppauper
Posts: 11729
Joined: November 15th, 2001, 1:29 pm

Re: Simulating MBS prices from durations

November 10th, 2017, 9:00 pm

Let's say I have two assets, [x] with a 2 duration and [y] with a 1 duration.
This implied the formula for line between these two securities' price movements is [x] = 2/1 [y] ...  which implies the beta is 2.  For the inverse, the beta would be 1.

Where I am getting hung up is that the durations seem to imply a perfect correlation between the two assets.  beta_xy = 1 / beta_yx.  This situation only holds if the correlation is exactly 1.
there are a lot of assumptions in there. To get the ratio of the price movements from the duration, you seem to be assuming something like a uniform shift in interest rates, and if you ignore the convexity they probably are perfectly correlated under those assumptions