# Which exact interest rate should I use for valuing equity index futures (ie. SPX, MXEA)?

I'm trying to build a model that values futures for equity indicies like SPX. For example, this product link here. I know that the model is simple (please correct me if I'm wrong):

$$S_{T} =S_{0}e^{(r-d)(t-T)}$$ where $$r$$ is the risk-free rate, $$d$$ is the dividend yield/equity repo/cost of carry, $$S_0$$ is the underlying price (at 4:30est for SPX), and $$S_T$$ is the $$T$$-maturity futures price as of $$t$$.

I'm struggling to use real world data to tie out to real world prices. I'm using Bloomberg data for the underlying, the $$t-T$$ point of the 3m LIBOR curve for $$r$$, and an interpolated value for $$d$$ using implied dividend yields from Markit dividend yield curves. That being said, the $$d$$ value is negligible (<0.2%), and should probably be excluded from this example to avoid confusion, but I kept it in for completion.

Surprisingly, I'm finding this to not tie out to real world end of day futures prices. Many days, I see prices move in different directions (i.e. futures price goes up by \$5 while the underlying went down by \$30). I would expect some noise in the calculation, but given how simple futures are, I would have assumed futures would move in the same direction as the underlying almost every single day. Am I doing something wrong here, or do I have unreasonable expectations of the market data + model?

• What "end of day prices" are you using? Up until 2020/10/23 the settlement price for S&P futures was the 16:15 NY (15:15 Chicago) price, while the end of day price for the index was the 16:00 New York price. Since 2020/10/26 both prices are 4pm NY prices. MAKE SURE YOU ARE USING SIMULTANEOUSLY OBSERVED PRICES FOR THE FUTURES AND THE UNDERLYING. Prices can move quite a bit in 15 minutes. Bloomberg in particular reports the setllement price for futures when daily prices are requested. – noob2 Jan 14 at 22:20
• "Bloomberg in particular reports the setllement price for futures when daily prices are requested" - this depends on your settings in GFUT under "94) Price Settings" – user42108 Jan 14 at 23:50
• True, I set GFUT a long time ago and never changed it, but it could be a different setting for you. Please check. – noob2 Jan 15 at 12:03
• Thanks @noob2! That's very helpful. I checked GFUT and it's set to settlement price. Fascinating that the settlement times changed recently. In fact, I running my model through that date, so errors are starting to make sense. – John Matok Jan 15 at 16:13
• You can red about the settlement time change here (it was announced in advance of course) cmegroup.com/education/articles-and-reports/… – noob2 Jan 15 at 16:19