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Nabil Kahale's Smile Interpolation Paper

June 2nd, 2020, 10:45 am


I was going through the 2005 paper on "Smile interpolation and calibration of the local volatility model" by Nabil Kahale (attached). He gives Algorithm A which he describes as in attachment 1. The c(j) and gamma(j) are mentioned in Theorem 3 of the same paper as in attachment 2.

Unfortunately I am stuck at step 2, not knowing how to initiate these values for the loop. Can someone, who has probably tried this method earlier, help me?

Thanks a lot!
Smile Interpolation.pdf
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atachment 2.png
Theorem 3
atachment 1.png
Algorithm A
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Re: Nabil Kahale's Smile Interpolation Paper

June 3rd, 2020, 12:49 am

Looked briefly, but got a headache. Your best bet might be to browse papers that cite it, and hope one of them helps you out.
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Re: Nabil Kahale's Smile Interpolation Paper

June 15th, 2020, 8:32 pm

What did the author reply when you asked him?
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Re: Nabil Kahale's Smile Interpolation Paper

December 20th, 2020, 12:04 pm

Not sure if this helps, here is an implementation of the C1 part for a single maturity.