RquantLib : FittedBondCurve function

Hi Oliver,

Simply add degree to curveparams, something like this

curveparams <- list(method="SimplePolynomialFitting", origDate = Sys.Date(), degree = 3)

'degree' is a parameter required for QuantLib's
SimplePolynimialFitting. I am terribly sorry that we neglected the
documentation on that (and possibly a few other parts :( ).


-k



On Thu, Nov 5, 2009 at 2:34 PM, Olivier Schmitt
<olivier.schmitt at gmail.com> wrote:

Allen - Thanks for the suggestions, especially the one about fitting
several parts of the curves separately. I thought the splines method
had high enough dimensionality so that there would be a very close fit
all along the curve.

Khanh - Well, thanks and great job on working on adapting QuantLib to
R, it is an extremely helpful project! I have two question for you
then :
?- I believe the maturities need to be integer, would there be a way
around this, so that, in particular, the part of the curve between 0
and 1 year could be fitted as well?
?- I tried the example of the help file with
method="SimplePolynomialFitting" instead of
"ExponentialSplinesFitting" and it made R crash. Do you have an
example for simple polynomial fitting?



On Thu, Nov 5, 2009 at 11:14 AM, Khanh Nguyen <knguyen at cs.umb.edu> wrote:

Hi Oliver,

I implemented RQuantLib's FittedBondCurve. I put your data through
FittedBondCurve.cpp (QuantLib/Examples/FittedBondCurve.cpp) and the
result follows that of RQuantLib. I don't know all the detail about
how quantlib does its curve fitting, so perhaps you will get better
explanation from QuantLib's mailing list.

knguyen at knguyen-laptop:~/Desktop/FittedBondCurve$ g++ -o newbond
FittedBondCurve2.cpp -lQuantLib -lm && ./newbond

Today's date: November 5th, 2009
Calculating fit for 15 bonds.....

(a) exponential splines
reference date : November 5th, 2009
number of iterations : 7264

Value for ts1 on November 5th, 2011
2.554127 % Simple continuous compounding
Value for ts1 on November 4th, 2014
2.659071 % Simple continuous compounding

Enclosed is the source code.

-k


On Thu, Nov 5, 2009 at 10:36 PM, Allen Kuo <allen_kuo at yahoo.com> wrote:

Olivier:

I've never used Rquantlib but the key to note for the underlying QuantLib code is that it is based on a multidimensional optimization problem- the mathematical solutions you get (and there may be multiple solutions to the problem- nonuniqueness here) may very well depend on where you inititalize your search (guessSolution_ in the code below).

http://quantlib.svn.sourceforge.net/viewvc/quantlib/trunk/QuantLib/ql/termstructures/yield/fittedbonddiscountcurve.cpp?revision=16281&view=markup

There are also iteration?numbers and lamda parameters to play with in the original code. You can even change the optimization method if you have the time.

Generally, that?two year point will get you a kink in the curve since it is more out of line with the other coupons. Since you are minimizing pricing errors subject to a duration adjustment (gives you approximately yield), my guess is a single outlier is probably never going to be fit well with this generic methodology. To pull the curve down closer to this point, you may have to artificially add other points close to this bond, with a similar coupon. Then the optimization will weight this part of the curve more (but now, to the possible detriment of other points on the curve....).

Generally, best fitting from 2 to 30 years accurately will not be easy- this is a global best fit, which may lead to local issues. May also consider just fitting 0-10 years separately from the longer tenors (10-30 years). For fair value pricing purposes, this may be a better bet.

Finally, note also you're comparing zero rates to the coupons (I think). This may not be the best comparison. Par rates should come closer to the coupons.

Best,
Allen


--- On Wed, 11/4/09, Olivier Schmitt <olivier.schmitt at gmail.com> wrote:


From: Olivier Schmitt <olivier.schmitt at gmail.com>
Subject: [R-SIG-Finance] RquantLib : FittedBondCurve function
To: r-sig-finance at stat.math.ethz.ch
Date: Wednesday, November 4, 2009, 6:33 PM


Hi,

I am trying to run an example based on the one provided in the
documentation for FittedBondCurve, from RQuantLib but using current
data.

library(RQuantLib)

Loading required package: Rcpp

lengths <- c(2,5,7,10,30)
coupons<- c(0.0090,0.024,0.03,0.035,0.043)
dateparams <- list(settlementDays=0, period="Annual", dayCounter="SimpleDayCounter", businessDayConvention ="Unadjusted")
curveparams <- list(method="ExponentialSplinesFitting", origDate = Sys.Date())
curve <- FittedBondCurve(curveparams, lengths, coupons, dateparams)

curve$table[2*365,]

? ? ? ? ? date? zeroRates? discount
730 2011-11-03 0.02553986 0.9502694

curve$table[5*365,]

? ? ? ? ???date? zeroRates? discount
1825 2014-11-02 0.02658928 0.8756396

So, it seems the output curve does not fit the short end data very
well. Are there further parameters that I could adjust to improve
this?

Thanks!

Olivier