Volatility smile fitting

monlavingia · July 12th, 2006, 10:25 pm

I have just begun to price a vanilla call under a VG process using FFT. In terms of calibration, is normal practice to calibrate the parameters (nu, theta,sigma) by non-linear least squares to the market call prices (i.e. min (C(sigma,nu,theta)-C(market))^2). Then obtain implied volatiities by reverse solving black-scholes. OR..Do you calibrate the parameters by non-linear LS so the difference in implied vol is minimised?

doublebarrier2000 · July 19th, 2006, 9:10 am

hi monlavingiai would be very interested to see how you are pricing a vanilla call under VG.Any chance you could send me something (spreadsheet etc.........)emailgw3@blueyobnder.co.uk

Flare1 · July 20th, 2006, 6:22 pm

I do this every quarter......back-solve (option analysis once you have the value of the option) to get the implied volatility then fit as many "knowns" into the smile as you can. Once you get enough data points you can interpolate the rest. I use a linear interpolation even though the vols usually are not linear if you get really far in or out of the money. It works for me. Besides, I think I am the only financial reporting accountant on this whole forum.