FINC6010 Chap.4 Forward and Futures Pricing
Forward and Futures Pricing
Forward pricing comes from comparing a contract with a replicating strategy, not from predicting the future spot price. This chapter builds cash-and-carry and reverse cash-and-carry trades, then adjusts spot value for financing, known income, proportional yield and foreign interest. It also separates the delivery price of an existing contract from that contract’s later value.
Cash-and-carry borrows funds, buys the asset, accounts for income or holding costs and delivers the asset at maturity. Reverse cash-and-carry reverses those legs when short selling is feasible. The relation is strongest for investment assets that can be traded and stored; consumption assets can carry convenience benefits that weaken simple equality.
Known cash income reduces the financed spot amount, while a proportional yield reduces the net carry rate. Currency pricing uses the domestic rate as financing and the foreign rate as yield, which makes quotation direction essential. After inception, the contract’s fixed delivery price remains unchanged even though a new forward price moves.
The value of the existing position is the discounted advantage or disadvantage of its fixed terms relative to current market terms.
What this chapter covers
- 01
Investment and consumption assets
- 02
Cash-and-carry replication
- 03
Short selling constraints
- 04
Known income and proportional yield
- 05
Currency forward pricing
- 06
Forward price versus contract value
Worked example · free
Price a forward with income
- 1Find the present value of income paid before maturity.
- 1Subtract that value from spot before carrying the net investment forward.
- 1Apply the stated interest and time convention.
- 2Report the delivery price and its units.
Key terms
- Investment asset
- An asset held significantly for investment and often amenable to arbitrage pricing.
- Convenience yield
- The non-cash benefit of holding a physical consumption asset rather than only a contract claim.
- Cash-and-carry
- A replication strategy that finances a spot purchase, holds the asset and delivers it against a forward so terminal cash flows can be compared.
- Delivery price
- The fixed price written into a forward contract for the maturity exchange, distinct from the contract's value after market conditions change.
- Short selling
- Borrowing an asset, selling it and later buying it back for return to the lender while compensating distributions and paying any borrowing cost.
- Forward value
- The current economic advantage or disadvantage of an existing forward with a fixed delivery price compared with current market terms for the remaining maturity. It is distinct from the delivery price quoted for a new contract. Discounting aligns the comparison date.
Forward and Futures Pricing FAQ
Is a forward price a forecast?
No. The standard pricing relation compares the forward with a replicating package using spot purchase, financing and carry. It identifies a no-arbitrage benchmark under stated assumptions. The realised future spot price can still differ from the delivery price.
How does income affect a forward price?
Income received by the asset holder reduces the net cost of carrying the asset to maturity. For known cash income, subtract its present value from spot before compounding. For a proportional yield, subtract the yield from the carry rate in the exponent.
Why do currency rates enter twice?
A foreign currency is an asset that can earn its own risk-free rate. The domestic rate represents financing in the quote currency, while the foreign rate acts like a yield on the underlying currency. Quote orientation determines which rate takes each role.
What makes an apparent arbitrage executable?
The price difference must survive bid-ask spreads, financing, storage, asset borrowing and contract specifications. Every leg must be available in the required quantity and timing. A frictionless theoretical gap can therefore sit inside a practical no-arbitrage band rather than produce a guaranteed trade.
Exam move
Write the replicating trades in time order before using a formula. Label the spot quotation, income timing, interest convention and maturity. After calculating, ask which arbitrage legs would apply if the market forward sat above or below the theoretical price and whether short selling is feasible. Build a small library of variants: no income, known cash income, proportional yield and foreign currency.
For each one, derive the sign from the cash flows before memorising the compact equation. Switch between effective and continuous compounding only after naming the convention, and check that time is expressed in years. When valuing an existing contract, circle its fixed delivery price so it cannot be replaced accidentally by today’s forward quote.
Finish every arbitrage explanation with the maturity cash flows and show that the unknown terminal spot price cancels. If borrowing fees, bid-ask spreads, storage constraints or short-sale limits are mentioned, discuss how they widen the no-arbitrage range rather than forcing an exact textbook equality.
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