METHODOLOGY
How implied opening prices are calculated from futures markets.
The Model: Cost of Carry
Under the cost-of-carry model, a futures price reflects the expected spot price after accounting for the time-value of money, dividends (or storage costs), and time to expiry:
Rearranging to solve for the implied spot price given today's futures price :
Inputs
For US indices (S&P 500, Nasdaq-100, Dow Jones, Russell 2000): continuous front-month contracts via Yahoo Finance (ES=F, NQ=F, YM=F, RTY=F). For international indices (FTSE, DAX, Hang Seng): scraped from Investing.com when Yahoo does not carry the contract. For commodities: Yahoo Finance commodity futures (GC=F, CL=F, etc.).
The last known index close or intraday level from Yahoo Finance. Used only to compute the implied change; the fair-value calculation itself depends solely on F, r, q, and t.
3-month US Treasury bill coupon-equivalent yield from the official Treasury.gov XML feed. Updated every 60 seconds. When the feed is unavailable, a recent fallback rate is used and a stale-rate badge is shown.
For equity indices and stocks: the trailing 12-month dividend yield of the index's proxy ETF (e.g., SPY for S&P 500), sourced from Yahoo Finance. For commodities: estimated annualised storage and insurance cost stored in our symbol registry. A negative q increases the fair value; a positive q (storage cost) decreases it.
Calendar days from now to the futures contract's last trading day, divided by 365.25. Expiration dates are computed from the contract's schedule (e.g., third Friday of the quarterly month for ES=F).
Expiration Schedules
| Instrument | Contract | Expiry Rule |
|---|---|---|
| S&P 500, Nasdaq, Dow, Russell | ES=F NQ=F YM=F RTY=F | Third Friday of Mar/Jun/Sep/Dec |
| Nikkei 225 | NIY=F | Second Friday of Mar/Jun/Sep/Dec |
| FTSE 100 | Investing.com | Third Friday of every month |
| DAX | Investing.com | Last Thursday of every month |
| Hang Seng | Investing.com | Last business day of every month |
| Gold, Silver, Copper | GC=F SI=F HG=F | Last business day on or before the 25th |
| Crude Oil, Natural Gas | CL=F NG=F | 3 business days before the 25th of prior month |
| Bitcoin, Ethereum (CME) | BTC=F ETH=F | Last Friday of every month |
Data Sources
Data is cached server-side for 60 seconds and streamed to clients via Server-Sent Events. Quotes may be delayed by up to 15 minutes depending on the provider.
Volatility Cone (1σ Range)
Alongside each implied opening price, we display a one-standard-deviation daily range derived from the CBOE Volatility Index (VIX). VIX expresses annualised implied volatility for the S&P 500 as a percentage; converting to a daily dollar move:
where is the implied opening price computed by the cost-of-carry model, and VIX is expressed as a decimal (e.g. 18 → 0.18). The resulting range gives a rough sense of overnight uncertainty baked into options markets. Note that VIX reflects S&P 500 implied vol and is only a loose proxy for other instruments.
Accuracy Tracker
After each trading session, the implied opening price (computed from futures pre-market) is compared against the actual market open. The miss is recorded as a percentage:
Yesterday's prediction error. Positive = model over-estimated; negative = under-estimated. A value near zero indicates a highly accurate prediction for that session.
Mean Absolute Error over the trailing 30 trading days. Direction-agnostic — measures average miss magnitude. Useful for calibrating how much confidence to place in the model's current projection.
