Jack: I do NOT use the SPX spot price in any of my option pricing or greeks, but derive the forward price instead from the option chains. (This way I can simplify the handling of dividends for my SPX greeks) This is working great for me. Since you can't directly trade SPX, and precise greeks using SPX spot is awkward at best, it may find few, if any, places where the use of the value is critical!
So you look at forward delta and gamma? How do you de-tangle the funding effects and that sort of stuff?
I hope I did not make a bold statement prematurely! I retract my "false" statement as I now have misplaced my ammo! ;-)
This means that the Price Return Index behaves like a normal stock, where the go down on ex-dividends. Similar with SPY. The price reflects the returns ex-dividends. The Total Return Index behaves in a way, where the dividends are reinvested. So effectively, when an underlying stock goes ex-dividend, the index drops, but then the dividend is added again to the index-level. So it gives the total return including dividends. So @stepandfetchit was correct. But good to point out the differences between price and total return based. Most indices are Price Return based, but for instance the DAX is Total Return based. So SPX (and ES) futures are generally traded below the index-level, because of future dividends. While the DAX futures trade at or above the index-level.
By examining the BID and ASK prices for all options of a chain, and discarding the outliers, such as those with BID < 50 cents {pick your poison}, then use PUT CALL parity to resolve the Forward price, you can get a pretty good fit. Below is a few I just ran (these will be off as the BID/ASK is wider now), but hopefully you can get an idea. Note: the interesting value is called "U", which is like a forward adjusted for Dividend impact (so no need to also resolve Dividend). I use the U in place of the underlying price for the BSM. Also, I use the R value for interest rate in BSM, similar for T (time), etc. You used some words that are over my head. So, it is possible my response does not fit your question! If so, I may need you to speak slower and use smaller words! ;-)
Do you agree that SPX-spot is a straight calculation from the components' prices? If so, then yes, when a stock goes ex-div its price will decline and this will be reflected in the value of SPX. Dividends only come into play insofar as they make the index go down when a stock goes ex-dividend. The option chain will reflect the price that SPX will be at expiration and that is why the effect of the dividend stream until expiration is reflected there. In other words, the ATM for the option is the SPX spot minus the effect of the dividends until expiration (ignoring interest rates for simplicity) At least that is how i understand it but of course I could be wrong cheers !
So, here's what the OP showed. First one is 10x SPY vs SPX index. Second is the 10x IVV vs SPX index, which is another S&P500 ETF. Both have a similar sawtooth, going up during the quarter and than drops. The drop IMO should be the amount of dividend paid by the ETF (x10 in this case). Which is roughly 1-1.10 per quarter. About 4.50 yearly... SPX pays about 45 yearly in dividends. SPY starts out below the index, and IVV starts out roughly AT the index level... which makes sense to me. So, to me it seems SPY is continuously undervalued by about 1. Is that maybe because it's a bigger ETF and there are more people shorting that compared to IVV?
Yes that's correct.... I think it's this sentence from your first post that's a bit confusing: "The numerical value of SPX is calculated by a formula that takes into account only stock prices (with no accounting for dividends whatsoever)" So yes, options are based on the future values of SPX index. Essentially priced of the SPX Futures, which is Index + Interest - Dividends...
My question was, how do you separate the dividend and interest rate risk from the spot risk? In short, do you assume that you will always delta-hedge with an appropriate combo? Or you don't trade far enough out for that to matter much?
Those are just the Futures right? So your 'U' would match the corresponding ES or SPX future... @sle, I think he means he's adjusting the greeks to the correct ATM level. Which isn't the index but the future..., but you know that