Inputs and Data Alignment for Equity Index Futures Valuation

Summary

The document presents a question about valuing equity index futures with a cost-of-carry model. The proposed inputs are the current index level, a risk-free interest rate over the contract horizon, and a dividend yield or related carry estimate. The author describes using market data for the index, a three-month LIBOR curve point, and an interpolated implied dividend yield, then finds that calculated futures prices do not consistently track observed end-of-day prices.

The key learning value is the model setup and the practical calibration problem it raises: even a simple relationship can fail to match market data when inputs, timestamps, or conventions do not align. However, the document contains no answers or investigation of the discrepancies. It does not establish whether the issue comes from rate selection, dividend estimates, timing differences between index and futures observations, contract details, or other market factors. It therefore serves as a prompt for model and data validation rather than a resolved valuation method, and its specific input choices should not be treated as endorsed conventions.

Key ideas

• Equity index futures valuation is framed through spot level, financing rate, and dividend or carry inputs.
• The author reports that calculated prices do not reliably match observed futures prices.
• Data timestamps and conventions are potential areas to investigate when model and market values diverge.
• The document provides no diagnosis or confirmed choice of interest rate.

Tags

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


# 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?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.