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fa
Posts: 10
Joined: December 10th, 2003, 11:07 am

### What is convexity?

bilbo1408
Posts: 179
Joined: August 3rd, 2007, 12:50 pm

### What is convexity?

It appears you have spent a good bit more time thinking about this than I have. I have learned that local quadratic approximation can be estimated using a Maclaurin polynomial such that f(x) ~ f(0) + f ' (0)x + (f '' (0)/2!)x^2 which is a good estimator in the neighborhood. However, this approximation does not improve much on the convexity calculation. Therefore, it is natural to ask whether one can improve on the accuracy of a local quadratic approximation by using a polynomial of degree 3. Specifically, one might look for a polynomial of degree 3 with the property that its value and the values of its first three derivatives match those of f at a point; and if this provides an improvement in accuracy, why not go on to polynomials of even higher degree? So, for your example stemming from the 360 yields of a 30 year mortgage, I am suggesting that your method is very similar to "finding" a 360 degree polynomial whose value and value of its first 360 derivatives match those of your bond/yield curve function at point f(x). The problem here is that I offer no method of "finding" that polynomial. I imagine that it would not be a simple task. Nevertheless, this has turned into a great discussion, and I invite someone to correct me......I am not certain that what I have suggested here is 100% correct.
Last edited by bilbo1408 on November 8th, 2007, 11:00 pm, edited 1 time in total.

dr3am0ne
Posts: 1
Joined: August 11th, 2008, 5:52 pm

### What is convexity?

quantmeh
Posts: 5974
Joined: April 6th, 2007, 1:39 pm

### What is convexity?

how to split the convexity of MBS into "pure" interest rate component and default component?when rates change, it causes changes in default rates too. changes in default rates change the interest income and principal amortization.... i.e. there there's higher order effects caused by defaults embedded in convexity. how to attribute a portion of convexity to defaults?

fa
Posts: 10
Joined: December 10th, 2003, 11:07 am

### What is convexity?

Last edited by fa on August 12th, 2009, 10:00 pm, edited 1 time in total.

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