Forward Price
Risk-neutral expected future spot.
The no-arbitrage future price of the underlying at expiry T under the risk-neutral measure. It's the correct center for option pricing — put-call parity and SVI surfaces are anchored to the forward, not spot.
r = risk-free rate, q = continuous dividend yield, T = time to expiry in years. Implied forward is backed out from put-call parity at each tenor.
- F > S (contango): r > q, typical for low-yield equities.
- F < S (backwardation): q > r, typical for high-dividend or hard-to-borrow names.
- F ≈ S: short tenor or r ≈ q — spot and forward indistinguishable.
API Reference
Why Forward Price Matters for Trading
Options are priced against F, not S. Using spot to build skew, delta targets, or SVI introduces carry-driven bias. Use the implied forward whenever dividends are uncertain.
- What it measures
- The no-arbitrage expected spot at expiry under the risk-neutral measure.
- What it signals
- The correct center for moneyness, skew, and greek calculations at a given tenor.
- Why we measure it
- Put-call parity, variance surfaces, and standardized moneyness are anchored to F.
- Who uses it
- Surface modelers, dividend-sensitive traders, long-dated option desks, arb checkers.
How to read Forward Price
- r > q
- Typical for SPY, QQQ, low-div names
- ATM strike shifts above spot
- Wider at longer tenors
- q > r
- High-div or hard-to-borrow names
- ATM strike shifts below spot
- Check hard-to-borrow rates
- Short tenor or r ≈ q
- Spot works as proxy
- 0DTE / weekly options
- Minimal carry impact
Rules of thumb
- Use implied forward when dividends are uncertain. Special dividends and announcement risk distort theoretical F.
- ATM = ATF, not K=S. "At-the-money" for pricing purposes means at-the-forward.
- Skew is in log(K/F). Computing skew against spot biases the slope in high-div names.
- F shifts with dividend announcements. Watch forward for corporate-action-driven moves that aren't in spot.
- Put-call parity breaks → arb flag. If implied forward drifts from theoretical by > bid-ask width, suspect data issues or hard-to-borrow stress.
Related Concepts
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