forward price

Forward Price

@gatheralVolatilitySurfacePractitioners2006 (Local Volatility in Terms of Implied Volatility)

The forward price is the agreed-upon price at time $t=0$ for delivery of an asset at a future time $T$ under a forward contract. In an arbitrage-free market, it is determined by cost-of-carry considerations.

For a non-dividend-paying asset, the forward price is

$$F_{0,T}=S_0{e}^{rT}$$

where $S_0$ is the spot price, $r$ the continuously compounded risk-free rate, and $T$ the time to maturity.

---

General Form (with Carry)

More generally,

$$F_{0,T}=S_0{e}^{(r-q)T}$$

where $q$ represents a continuous yield (e.g. dividends, convenience yield, or foreign interest rate in FX).

---

Properties

• No-arbitrage condition:
  Ensures equivalence between holding the asset and replicating it via financing.

• Deterministic at inception:
  Unlike the future spot price $S_T$, the forward price is fixed at contract initiation.

• Relation to log moneyness:
  Forward log moneyness is typically defined as $\ln (F_{0,T}/K)$, making the forward price the natural reference in option pricing.

---

Role in Financial Theory

Forward prices are central to derivatives valuation, particularly under risk-neutral pricing, where discounted asset prices are martingales. They provide the natural numéraire-adjusted expectation of future spot prices in models such as the Black–Scholes model.

---

Disclaimer

This content is AI-generated for informational purposes and may not constitute authoritative academic guidance. Verification from primary sources is recommended before use.
Generated on: April 1, 2026