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): real-time CME front-month contracts via Charles Schwab (/ES, /NQ, /YM, /RTY), falling back to Yahoo Finance. For international indices (FTSE, DAX, Hang Seng, Nikkei 225): scraped from Investing.com. KOSPI 200 uses the KRX day future via Naver realtime (it doesn't trade overnight, so near the Korean pre-open it reflects the prior settle; a lagging feed falls back to the cash index). TAIEX comes from the TAIFEX exchange API. For commodities: front-month futures via Schwab / Yahoo Finance (/GC, /CL, 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.
The short-term risk-free rate of the currency each index is denominated in — because the cost of carry finances the underlying basket in its own currency, so the discount must use that currency's rate (not a single global one). Live sources: USD = Treasury.gov 3-month bill; GBP = Bank of England SONIA; EUR = 3-month Euribor; HKD = HKAB HIBOR; TWD = TAIBOR — all daily fixings. JPY and KRW have no free daily feed (TIBOR is a daily PDF, the Korean CD rate is key-gated), so they use the OECD 3-month interbank series via FRED — monthly, with a one-to-two-month publication lag, but live and auto-updating rather than a frozen constant. Each rate falls back to a recent constant if its fetch fails or goes stale, and rates are refreshed a few times a day. Using one US rate for every market — as earlier versions did — biased non-USD implied opens by up to tens of basis points and could even flip the predicted direction on longer-dated contracts.
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. Total-return indices are an exception — the DAX reinvests dividends into the index itself, so its carry uses q = 0 (subtracting a dividend yield would double-count). 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 /NQ /YM /RTY | Third Friday of Mar/Jun/Sep/Dec |
| Nikkei 225 | Investing.com | 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 |
| KOSPI 200 | Naver realtime (KRX day future) | Second Thursday of Mar/Jun/Sep/Dec |
| TAIEX | TAIFEX | Third Wednesday of every month |
| Gold, Silver, Copper | /GC /SI /HG | Last business day on or before the 25th |
| Crude Oil, Natural Gas | /CL /NG | 3 business days before the 25th of prior 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 that market's own 30-day implied-volatility index. Each index expresses annualised implied volatility as a percentage; converting to a daily dollar move:
where is the implied opening price computed by the cost-of-carry model, and the volatility index is expressed as a decimal (e.g. 18 → 0.18). The resulting range gives a rough sense of overnight uncertainty baked into options markets. Each card uses its own exchange's vol index rather than a single proxy — the US indices use the CBOE VIX, while international cards use their native equivalents: VKOSPI (KOSPI 200), TAIWAN VIX (TAIEX), the Nikkei 225 VI, VHSI (Hang Seng), VDAX-NEW (DAX) and VFTSE (FTSE 100). Where a native index is unavailable, the card falls back to the US VIX.
Accuracy Tracker
Each index is predicted in its own venue's pre-open window and scored against that session's actual open — so London, Tokyo, Seoul, Taipei, Hong Kong, Frankfurt and New York are each measured against their own open, not a single US clock. 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.
Several markets open via a call auction whose first published print sits near the prior close until constituents trade. For those (FTSE, DAX, Nikkei, TAIEX) we score against the settled level ~15 minutes in rather than the stale opening tick. Where an exchange publishes an official opening-auction price (KOSPI 200 and TAIEX), we use that authoritative value as the actual open.
