# Options pricing model inversion

He cited about Roll's compound formula for finding the lead-lag effects between stocks and options. I have a similar data for National Stock Exchange's Index, NIFTY but it's daily, not intra-day. I could not understand what Roll, and Matthew did. If anyone could explain the inversion of this pricing formula, it'd be a huge help.

• After mentioning that Stephan/Whaley and Diltz/Kim inverted the Roll formula, O'Connor says that "in this study" he did not do this (giving a reason) but instead he inverted the Binomial Option Pricing method with Dividend. So which method is your question asking about? The BOPM seems better since it correctly handles both the dividend and the American exercise, the Roll method only approximates the effect of the dividend. – noob2 Jun 13 '20 at 21:31
• @noob2 I am asking about the BOPM model. I didn't get how the BOPM model was inverted. Please tell me how to proceed with it. – tanvinagpal98 Jun 13 '20 at 22:36
• You have $\sigma,r,T,K,Div$ and the market prices $S_{MKT}$ and $O_{MKT}$ (the option). Initialize $S^*$ to $S_{MKT}$. Calculate the option price $O_{BOPM}$ from $S^*,\sigma,r,T,K,Div$, if it is equal to $O_{MKT}$ stop. If not, adjust $S^*$ up or down a little (based on Black Scholes Delta) and try again the BOPM calculation with this new implied stock price. – noob2 Jun 14 '20 at 7:55
• @noob2 Could you please explain it with an example. I am a bit new to this. – tanvinagpal98 Jun 17 '20 at 21:35