mrbadguy,It seems that the file (Adams.zip) contains error. It can't be extracted. The message was that the file seems to be invalid file. Could you resend it again?

tigorI did not encounter eny problems with opening adams.zip ...BUT try opening yieldcurve2.zip. It also contains Ken's paperKane

Sorry for borrowing this thread!In an attempt to understand bootstraping, I had tried to debug a project - Quantlib which goes into bootstrapping for valuation of swap options.But the most confusing thing to me is after days of debugging into bootstraping,I am not able to understand if it is the Nelson-Siegel method, or the Cubic spline method? Instead it goes into some Brent's method.Is Brent's method a different new approach,or is it a subalgorithm for any of the above 2 methods?Thanks,asd

asd, Brent's method is an algorithm for finding the minimum of a function (of one variable) by parabolic interpolation and discussed in Numerical Recipes (chapter 10.2), so it's probably a subrutine for Nelson-Siegel. NS depends on several variables, but you can remodel it so that if you know tao, the problem is solved using linear regression. The problem could thus be reduced to a single variable problem, searching for the optimal value of tau.

"Risk Magazine has an article a year or so ago that outlined the different methods in widespread use. I think the author was from City Hall (that is, Bloomberg) "Has anybody an exact reference for this article? I've looked on Risk's search engine, without success. But that engine only goes back to Jan 2002. Perhaps it was before that? By the way, there are strong mathematical reasons why the method of Adams (quartic spline) is the best. But the algebra is a bit hairy.....

I am now prepared to eat humble pie .. the algebra of quartic splining is ideed hairy, although the Fortran/C/C++ recipes ("Numerical Recipes in ..." ) are very useful. (The code as well as the books are available, legally and for free, on the internet.) But the results of the quartic splining are, well, not premier league... ok for a curve with lots of nodes, but then, any method under such conditions would be pretty much ok. I have a curve (30 years) with maybe 10 nodes. The quartic spline looks like a rollercoaster - even negative rates in places! The start of the curve can be a bit bumpy and then the smoothness just takes over. Up and down, like a rollercoaster.Recently I found an approach of Bloombergs and Yekutieli (one of their quants) who tries to minimise the length of the forward curve subject to some smoothness. That strikes me as a very attractive idea. Has anybody had any experience or joy with such approaches? Are Bloombergs still using that approach?

I have estimated the term strucuture of China's bond market( can be downloaded for free from efinance.diy.163.com, but in Chinese). I have one experience that we should some different methods to estimate the term structure at the same time to choose the suitable parameters so that we can fit the data well. for examples, for spline approximation, we should decide the parameters of period division,etc.

I did a few experiments with the article written by Ken Adams to bootstrap a yield curve, and I am not too happy about the results (it's an euphemism!!!).The article is very clear about how to construct the splines and retrieve the yield out of the forward curve, but it doesn't suggest explicitly a method to choose the instantaneous forward rates at the nodes of the spline to match the market yield rates (bootstrapping is not possible, since the value of a spline depends globally on all points of the curve....)What is the best way to do so?The method that I implemented is simply a linear regression algorithm. I have n instruments chosen between cash instruments, and spot starting swaps. I assumed that having "n" instruments with same start date and "n" different end dates, my forward curve could be obtained with "n" nodes, one for each end date.At this point, my algorithm simply choses a forward curve that minimises the sum of the (absolute value of the) relative errors between the market rates of the instruments and the computed rates. In practise it's a usual least square problem, where the variables are the "n" instantaneous forward rates.The result is a forward curve that oscillates very wildly. I am trying to add a penalty function to force the forward curve to be smoother, but I am finding hard to set the sensitivity correctly. Could anyone suggest me alternative methods? Or just give me an idea on whether or not I am following the right track?Thanksgc

I believe the method is bogus. I say this with my hand on my heart, and after much implementation work, and being an ex-disciple. Even with modest oscillation of yields one gets dramatic oscillation in forward rates, even negative forward rates.One way to implement the method is to work out what the rates must look like if the forwards are quartic (of course, each rate spline is of the form K/t + quartic, so that f(t) = d/dt r(t)t is guaranteed). One gets the usual thing, where there are about 3 or 4 free variables left, and as usual one takes up these variables with the left hand second derivative is 0, the right hand first derivative is 0, whatever. I tried many variations, without success. One will notice in the article of Adams, one degree of freedom is left, unresolved.

Have you guys seen this paper? Computing Maximum Smoothness Forward Rate Curves I've been curious about the Adams/Deventer method since reading their paper, but to date I've done no work on this. The attached paper suggests that a cubic term is missing from the Adams 4th order polynomial.

QuoteOriginally posted by: GraemeI believe the method is bogus. .Thanks Graeme, mh.... I have spent quite some time implementing the ideas of the article, but if your experiements too haven't been very successful, it might be better for me to look at some alternative strategies.Have you got any suggestions (and articles) for alternative ways to interpolate the yield curve? At present I am using the common linear interpolation of logs of discount factors, but I am looking for alternatives. Someone suggests using splines for the log of the discount factors. What is the general feeling in the forum? Has anyone any article on how to do it in practical terms? (again, bootstrapping is not feasible, and I am thinking again of a least square problem...).Any other ideas that I might want to investigate?Thanksgc

QuoteOriginally posted by: AthleticoHave you guys seen this paper? Computing Maximum Smoothness Forward Rate Curves I've been curious about the Adams/Deventer method since reading their paper, but to date I've done no work on this. The attached paper suggests that a cubic term is missing from the Adams 4th order polynomial.I know that in the earlier versions of the Adams - van Deventer paper, there was this missing term. However, it was corrected subsequently, I think by the time it was published, it had been corrected. However, the original version was around for quite some time - presumably there was a big time gap - and (unfortunately, I guess) that is more often than not the version people refer to.

QuoteHas anyone any article on how to do it in practical terms? (again, bootstrapping is not feasible, and I am thinking again of a least square problem...).Any other ideas that I might want to investigate?You've got me a bit confused here... do you want a method that fits the inputs exactly, or a method that produces a smooth curve with some error term as small as possible? All of the methods we have been talking about so far are the former, but you seem to be interested in the latter? If the former (I know nothing about the latter class, for example, fitting to interest rate model such as Vasicek model or CIR model) then splines are the way to go. The splines need to be local, not global (i.e. not the usual cubic (or quartic!) spline, as a change in one place causes peturbations far away). Bezier splines (often called Hermite splines) is a good start. However, such methods do not have an explicit guarantee that the capitalisation function is monotone (== forward rates are never negative). For this, one needs monotone preserving interpolation.

Thanks Graeme for your patience.. I am looking for a method that fits the inputs exactly. I already have one (actually a few but the others are just too crude to be used for pricing) that does the job, but I am starting to get some complaints with some instruments, and I am trying alternative interpolation types to improve it.We get from our swap desk the swap rates up to 10y, and then 12y,15y,20y,30y,40y,50y. Up to 20 years we have relatively many instruments, so the interpolation method doesn't seem to make a large difference and I am happy with our results. When we look at instruments starting after 20y, then the interpolation becomes more and more important. In particular, if we try to price a swap starting in 30y or 40y with a length of 5y or less, we see significative differences from our counterparties, and I am getting some complaints too.At present we simply bootstrap, and in doing so, we find the intermediate rates by linearly interpolating the logs of the discount factors.The article by Adams made me think that a better solution would have been instead of generating a instantaneous forward curve that is smooth and that at the same time matches the observed values for the swaps. The only problem, is that since the instantaneous forward rates are not observable, and since Adams suggests using quartic splines (that depend globally on all the points), I was left without clear idea on how to replace the bootstrapping with an alternative algorithm... Least square minimisation is the only option that came to my mind (and my hope was that since I have n instruments and n forward rates, least square minimisation should return with a zero residual error. But this doesn't happen... the optimiser generally notices that the rate of improvement collapses and always returns with some very unstable result with a positive sum of errors).Adams himself shows how to retrieve the zero rates from a splied instantaneous forward curve, and claims that it returns good swap rates, but in the article I have doesn't give any hint on how to compute the instantaneous forward rates in first place ....This is why I mentioned least squares; lack of alternative more than anything else... What alternative ideas should I look at?Thanksgc