May 5th, 2014, 8:09 pm
I'm coming to this thread after a large break (9 years?) However I thought my experience might be interesting to anyone who finds this discussion after struggling with the Hull, Nelken, White paper. I burned a couple of days trying to resolve equations 8 & 9 and somehow back-out the L and sigmaA values from the known IVs. However, it so happened that I had Gatheral's "The Volatility Surface" on my desk and sure enough, he has an excellent discussion of this topic. His approach is, IMHO, more robust in that he draws values from all OTM puts, not just the 50 and 25 deltas. However, he also provides a worked example from which I was able to confirm my understanding of the approach using Excel's solver and some IV data from oX. Gatheral is well worth the read if you don't already have it (why wouldn't you?)