When a Forward Price Equals the Spot Price Divided by a Bond Price

Summary

The document asks whether a forward price for a financial product can be expressed as its current price divided by the price of a zero-coupon bond maturing at the settlement date. The proposed argument uses a conditional expectation under the maturity-forward measure and the claim that the appropriately discounted product price is a martingale under that measure.

The document contains no answer, derivation, or conditions establishing when the expression holds. In particular, it leaves unresolved what properties the product must have, whether it pays income or other cash flows, and how its price process relates to the chosen numeraire. It therefore serves as a question about risk-neutral valuation and measure changes rather than a complete pricing recipe. Readers should treat the stated equality as a hypothesis requiring assumptions about the tradable asset, financing, cash flows, and absence of arbitrage; none are supplied or tested in the text.

Key ideas

• The question proposes relating a forward price to spot value through a maturity bond price.
• Its argument relies on a martingale property under the maturity-forward measure.
• The document does not provide a derivation or answer confirming the proposed formula.
• Asset cash flows and the assumptions behind the pricing measure remain unspecified.

Tags

# Forward contract on a given financial product $P$


# Forward contract on a given financial product $P$












I would like to know whether my reasoning is correct or not.

Let $\pi_t$ be the price of a financial product $P$.

The forward associated to a forward contract on $P$ that settles at time $T$ is given by : $$F_{t}=\mathbb{E}^{T}\left(\left.\pi_{T}\right|\mathbb{F}_{t}\right)\\ =\mathbb{E}^{T}\left(\left.\frac{\pi_{T}}{B(T,T)}\right|\mathbb{F}_{t}\right)\\=\frac{\pi_{t}}{B(t,T)}$$

Since $\frac{\pi_{t}}{B(t,T)}$ is a martingal for $0\leq t\leq T$ under the $T$-forward mesure.

If not, under which conditions on $P$ this expression is correct ?

Thanks!

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