Re: cubic interpolation

Posted by Luigi Ballabio on Feb 05, 2015; 11:19am
URL: http://quantlib.414.s1.nabble.com/cubic-interpolation-tp16205p16232.html

Apologies for the delay; I didn't find the time to go back and check the math. I see from <http://www.wilmott.com/messageview.cfm?catid=4&threadid=98075&forumid=1> that you solved the issue, though. Is this correct?

Luigi

On Thu, Jan 29, 2015 at 5:59 AM, Sk Wong <[hidden email]> wrote:

Hi,

I have a question on the setup of the tridiagonal system in the cubic interpolation (under the choice 'Spline' for derivative approximation.  The tridiagonal system looks a bit different from the one suggested in the literature.  In particular, the middle components of the vector tmp_, the right hand side vector of tridiagonal system, are caculated as:

                std::vector<Real> dx(n_-1), S(n_-1);

                for (Size i=0; i<n_-1; ++i) {
                    dx[i] = this->xBegin_[i+1] - this->xBegin_[i];
                    S[i] = (this->yBegin_[i+1] - this->yBegin_[i])/dx[i];
                }

                // first derivative approximation
                if (da_==CubicInterpolation::Spline) {
                    TridiagonalOperator L(n_);
                    for (Size i=1; i<n_-1; ++i) {
                        L.setMidRow(i, dx[i], 2.0*(dx[i]+dx[i-1]), dx[i-1]);
                        tmp[i] = 3.0*(dx[i]*S[i-1] + dx[i-1]*S[i]);
                    }

Following the literature, one instead has (e.g. see Eq. 6.62 in Piterbarg-Andersen book V1 Chapter 6 Appendix):

tmp[i] = 6.0*(S[i] - S[i-1]);

Am I missing something here? Or any reference you can point me to which derive what Quantlib implements?

Thanks,

SK

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