Thank you Alan. The method in white paper "The CBOE Volatility Index - VIX"generate a better result on BS implied vol. It's not a very smooth curve, but I can see some oscillations of volatility between 25% and 27% for options with long expiration days.1.However, I can not understand well the logics behind this method. 1.1 Why only OTM options are considered? Is it because they are traded more actively?1.2 Why do they calculate foward price," by identifying the strike price at which the absolute difference between the call and put prices is smallest"? Is it because the long and short side has the smallest disagreement on this strike?I calculate implied dividend like this Forward_imp=S0*exp[-(r-q)*T],where Forward_imp is calcluated from the white paper. S0 is the spot price, r is the fixed risk-free interest rate, T is time to expiration, q is the implied dividend to calculate. 2.On this BS surface, I try to calibrate it with Heston model, but I find the Heston model is very sensitive to my initial guess. By different initial guess, one parameter can be abnormal, say kappa reaches 1.0e-5, or sigma reaches 1.0e-5, or rho equal to -0.9999. Is this because of some option prices are arbitragable (I can obsever arbitrage on the quote indeed)? I think a fast cure is to add constraints to the parameters.
Last edited by EdisonCruise
on March 24th, 2015, 11:00 pm, edited 1 time in total.