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.

  • $\begingroup$ 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, 2021 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, 2021 at 4:15
  • $\begingroup$ @noob2 yes,but the price of the index still drops after dividend paid $\endgroup$
    – MikeD
    Apr 6, 2021 at 4:16

1 Answer 1


SPX does not pay dividends, and VIX is based on SPX options


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.