"There are stochastic volatility models out there to overcome this problem." I see you've read the SABR paper
Interesting. The model really should be called the Black model (leave out the scholes). Black was the brains behind this not scholes. Or, the Black-Merton model.
I remember NOVA created a great 60M video called "Trillion Dollar Bet" a while back. It was an informative program about Fisher Black and Myron Scholes and how they came up with the Black-Scholes formula and also their involvement with LTCM and its failure.. I am sure most libraries probably carry a copy of that video if anyone is interested in seeing it..
nitro, You also may want to dig through wilmott forum. There maybe lots of interesting discussions about SABR and BS.. http://www.wilmott.com/index.cfm
McCloud, Thanks! That's where I found it! Do you know if someone has written a small program with sample data so that I can follow along and see if I understand the model? Or equivalently, some data and what the smile/skew curve would look like ? (assuming given the inputs of alpha, forward, k, beta, volvol, rho and time) nitro
I have a small spreadsheet I wrote to test it - i will look if i can find it. The great thing about SABR is the stability of vega hedges - some nameless company (starts with N and ends with A) made a lot of money using SABR.