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The VIX white paper (https://cdn.cboe.com/resources/vix/vixwhite.pdf) step #1 (page 6) says the the Forward Index Price is calculated as:

F = Strike Price + e^RT x (Call Price - Put Price).

Why doesn't it take dividends into account? Many of the S&P 500 stocks pay dividends, so isn't this formula going to over-estimate the forward index level?

I thought forward price is calculated using put-call parity:

C - P = D(F - K).

C: call price for strike K
P: put price for strike K
D: Discount factor (takes dividends and interest rates into account)
F: forward price
K: strike

The VIX seems to ignore the dividends portion of the discount factor.

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  • $\begingroup$ Assume the fair strike of the forward with maturity $T$ is $F$. At $t=0$, we borrow $C-P$ now and use this amount to go long a call struck at $K$ and short a put struck at $K$ and simultaneously sell a forward of maturity $T$. At maturity $T$, we collect $S_T-K$ from our options position and collect $F-S_T$ from forward position and repay our loan by paying $e^{rT}(C-P)$. By no arbitrage, the fair strike of the forward follows $(S_T-K)+(F-S_T)-e^{rT}(C-P)=0$, which implies $F=K+e^{rT}(C-P)$. $\endgroup$
    – ryc
    Apr 5 at 8:31
  • $\begingroup$ @ryc thanks. Makes perfect sense based on how you described it. I guess what I'm caught up on is this: if you use the forward price as calculated from the above equation in a model like Black Scholes, you typically get a different IV for the call than for the put. In order for them to have the same IV, you typically have to use a lower value for the forward price. $\endgroup$
    – MikeD
    Apr 6 at 4:15
  • $\begingroup$ @noob2 yes,but the price of the index still drops after dividend paid $\endgroup$
    – MikeD
    Apr 6 at 4:16
  • $\begingroup$ You are right, I deleted my comment. $\endgroup$
    – noob2
    Apr 6 at 4:37

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