Hi everybody,Here is the problem I'm currently fighting with these days.I have a set of american options prices on S&P 500 index from CME market ( but no european prices !) . I would like to use Barone-Adesi Whaley approximation formula to get the implied vol of these options but unfortunately I realise that this cannot be done directly because in this formula, I have to solve an equation to find S* first which depends on the implied vol. Consequently there can be multiple (possibly infinite) choice of implied volatitly that can match the price of a particular option at a given Strike.Usually people have the implied vol of european option and then solve for this volatility the equation that gives S* and finally find the approximation of the price of the american option they are trying to evaluate. Here I can't do that because I don't have the european volatility in the first place.Is there any trick that could eliminate this problem Thx for any insight

Hi Bridge,you can do this numerically and I think it is not much different than inverting BS.You just need a root solver and in each loop you're able to calculate the critical price S* with your current guess for the volatility.Regards

Yes this procedure might work in particular if the following is true :The B-A-W Price is something like (for a call) :C(S*(sigma),sigma)=Call_lMarketPriceso if S*(sigma) is an increasing function of sigma ( which I think is true ) and C(x,y) is increasing in both x and y then there can be at most one solution to the implied volatility problem.The fact that C(x,y) is increasing in x is not clear to me right now but the fact that it is increasing in y ( i.e. an option is vega positive) seems correct.I have to check this but as I was trying to solve the problem before doing the calculation I had not seen the problem in this wayThank's Balmung