Consider the case of using Black&Scholes model for extracting the individual strike/expiration IV for known Option prices. (Solve for IV) 1) Assume we are solving for IV, which is the big unknown. 2) Since we are solving for each Expiration, would it not be logical, and possibly more accurate, to use the Forward price of SPX, and ignore interest and dividends, as they are "baked in" to the Forward price? (Theory: Substitute forward price for spot price, for using B&S) The forward price may be extrapolated from the ATM option prices (as is done by CBOE per their VIX white paper "The CBOE Volatility Index - VIX®") or extrapolated from the ES Futures prices, adjusting for expiration. @rmorse: is this similar to your recollection for what may make sense here? (Thanks for your insight and feedback, which has been instrumental in my research).
I'm not sure what your questions is. Are you trying to predict the option price for a specific options in the future? Eg. SPX JULY 2000 puts 12 days from now?
Nothing so complex! Merely considering most ideal values (forward price corresponding to the option contract expiration primarily) appropriate for use in the B&S model, when solving for IV (ie, solve for which IV input results in observed price). I "THINK" this approach is in agreement with comments you have made previously regarding using the forward price instead of the SPX Spot price, when not at expiration of the option. Since I "missed this" previously, I would like to insure I am on the correct track!
May I ask what you want to use it for? Seems like a lot of work without an expectation of profit from it. How can you monetize what you are trying to calculate.
I thought the forward price (discount factor) is already accounted for when you use BSM: The auxiliary variables are: is the time to expiry (remaining time, backwards time) is the discount factor is the forward price of the underlying asset, and
Robert: I think I already have my answer. I am seeking to improve the accuracy of my derivation of IV for SPX options. Since the CBOE clearly uses forward pricing, instead of spot prices for SPX in their derivation of VIX (which I have replicated to insure I understand), I think I am on the right track. This also seems to agree with information you previously relayed in another thread, which I am at your debt for pointing out. (I was attempting to use SPX spot pricing for B&S model price input, which you clarified was only accurate at expiration--I now agree with you) As for as "monetization" goes, that is a down-stream possible outcome, but beyond the scope of this thread. {Too many moving parts to present here.}
A penny for your thoughts and accumulated wisdom with regard to "albeit with a little bit of care..."?
Well ... When you put it that way ... ;-) Unfortunately: I looked at: Black–Scholes formula[edit] A European call valued using the Black–Scholes pricing equation for varying asset price S and time-to-expiry T. In this particular example, the strike price is set to unity. The Black–Scholes formula calculates the price of European put and call options. This price is consistent with the Black–Scholes equation as above; this follows since the formula can be obtained by solving the equation for the corresponding terminal and boundary conditions. The value of a call option for a non-dividend-paying underlying stock in terms of the Black–Scholes parameters is: Both are true, however, using Forward pricing (F instead of S), seems to be path of least resistance in increasing accuracy (IMHO)