The dividend yield and interest rates used now match the stock price and the time remaining to maturity. Since this example is modeled for the same option on the same day, the rate is the same but the dividend is adjusted for the stock price to caculate the forward spot for the option.

First thing needed was more accurate forward price modeling for a single option. Began with intra-day prices. Started with 3 chains downloaded on the same market day for a SPY 105 strike. Notice in image below the model (at the top of the image below) calculated the forward spots for the options when S=110.09 @ 2.22 and for S=110.14 @ 2.21 while the actual market prices are 2.18 and 2.14.

Not bad but still no cigar cause the combo P/Ls to be modeled will allow for multiple contracts and up to five options. The problem is the current model is using the same IV (.4476) for all the (18 day put) options.

Since

**chain IVs are priced to the Strike**and

**model prices to the Stock**, an approach was needed to make the strike IV on the chain being used to model the forward prices close to the IV on the actual market chains with the prices the model was being tested to. Using the closed form pricing constants where S = Stock Price and X = Strike price and whole lot of hacks and failures, finally landed on the solution (called SEX and EXCESS ) below:

The image below show the results stepping (in pennies each of the three market chains (S=109.43, 110.09 and 110.14) the 105 put from closer to the money, S=109.43, to "furthest" from the money, S=110.14. The 110.09 prices both directions. The S=109.43 prices (only) away from the money/ The S=110.09 prices both directions. And, the S=110.14 prices (only) towards the money:

What surprised most was the the IV's, although they are heading in the right direction, are as much as 20 cents off the market IVs, BUT, the prices calculated with the forward IV's are much closer to the market prices than the "current" model using a static IV.

BTW, I do have a "kludge" that will bring the forward IV's much closer to the actual IVs. Also, since these are "free" chain options, the prices for the options might be priced to a different market price for the stock.

Someone told me I had found "sticky delta". Is anyone aware of published documents that might offer a better understanding of the processes involved in addressing this issue.

Any advice appreciated. Thanks!