November 9th, 2011, 3:08 am
OK, without any smoothing, I suppose the absolute simplest first try would be and where are the forward and backwards first order derivative approximation to f '(K_i).The f(K_i) are e^(r T) x the out-of-the-money option prices (bid-ask midpt) at strike K_i.This is just a standard 3 pt difference formula for f ''(K) on a non-uniform grid. Needs an endpt modification, of course, and probably a slight renorming to get unit total mass,and assumes clean quotes. If that one ever proved to be non-positive, then agree that some higherorder interpolation is called for, or grosser smoothing as discussed.
Last edited by
Alan on November 8th, 2011, 11:00 pm, edited 1 time in total.