An arbitrageur follows two rules: never use your own money, and never take price risk. Every forward, futures, and swap price in this lesson falls out of those two constraints.
These two words mean different things for forward commitments, and the exam punishes candidates who blur them. Pricing means finding the fixed price or rate that makes the contract worth zero at initiation. Valuation means finding what an already-live contract is worth today, in currency units.
At initiation, for an at-market forward. The forward price is chosen to force that. After initiation, spot moves, and the contract accumulates positive or negative value.
KEY: Price is a rate or a level fixed in the contract. Value is a currency amount that changes daily. A question asking "what fixed rate makes this swap fair today" is pricing; a question giving you an off-market rate from two years ago is valuation.
Suppose you sell a forward on an asset. To offset the exposure, you borrow , buy the asset, and carry it to expiration.
Common mistakes
- Compounding dividends from time zero. Each dividend earns interest only from its payment date to expiration, so the exponent is , not T. Using T on the $10 dividend in Example 1 gives $10.1227 and a forward of $1,002.15, a planted distractor.
- Treating the forward price as an expectation. Candidates adjust upward because they are bullish. The carry model uses only spot, rate, time, and carry cash flows.
- Forgetting to discount the FRA settlement. The rate differential accrues over the forward period but settles at expiration. Skipping the factor overstates the payment. On a $10 million notional, 90-day FRA with a 40 bp differential, the undiscounted $10,000 becomes about $9,900 after discounting.
Bottom line
- Generic forward price: F0 = FV[S0 + CC0 − CB0]; with continuous rates, S0 × e^((rc + CC − CB)T)
- Forward value at time t: PV of (Ft − F0), equivalently St − PV(F0); the short value is the negative
- Equity forwards subtract each dividend compounded only from its payment date to expiration; index forwards use a continuous dividend yield
- FRA fixed rate is the implied forward rate from the spot curve; settlement in advance is discounted by 1/(1 + Dm × tm)
Exam shortcut
Read the stem for the word "initiation." If it is there, you are pricing: solve for the rate or price that zeroes the contract. If the stem gives you a date after inception plus an old fixed rate, you are valuing: build the difference in rates or prices and discount it. For any swap, write the fixed-rate formula once.
The full lesson (about 3,579 words, 24 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.
Learning objectives
- forward commitments
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