FNCE30007 Chap.3 Forward and Futures Pricing
Forward and Futures Pricing
Define cost of carry
The course material gives this chapter a concrete anchor: Lecture 3 derives forward and futures prices for assets with no income, known income and known yield.
That cost of carry anchor controls how cash-and-carry arbitrage is explained and how continuous compounding is tested in changed practice.
Forward and Futures Pricing is a quantitative decision problem built from cost of carry, cash-and-carry arbitrage and continuous compounding.
The aim is to derive forward or futures price from spot, rates and income; a numerical result earns meaning only when the variables, units, assumptions and comparison are all explicit.
Begin with cost of carry: state what quantity it represents, the scale on which it is measured and the condition under which it changes.
Then map every symbol in the Forward and Futures Pricing formula checkpoint to cost of carry before calculation begins.
Formula checkpoint: cost of carry
Spot is carried at financing rate r net of continuous income yield q to maturity T.
Trace cash-and-carry arbitrage
Next connect cash-and-carry arbitrage to the calculation.
Show the cash-and-carry arbitrage transformation line by line, preserve units and signs, and make any denominator or baseline visible. A cash-and-carry arbitrage calculator output is not a method; the reader must be able to reconstruct why that operation answers the question.
Use continuous compounding to interpret or stress-test the result.
Ask whether the continuous compounding magnitude is plausible, whether a boundary case behaves as expected and which conclusion would reverse if an assumption changed. This is where computation becomes analysis rather than arithmetic.
When the task is to derive forward or futures price from spot, rates and income, separate inputs supplied by the problem from quantities you derive.
Then report the continuous compounding result in the language of the course and attach the relevant uncertainty, limitation or decision consequence.
Test with continuous compounding
Build a representation check before solving.
Put cost of carry, cash-and-carry arbitrage and continuous compounding into a small symbol-and-units table, mark which values are observed and which are calculated, and predict the direction of the result before doing arithmetic. A sign, scale or unit mismatch in cost of carry then becomes visible at setup instead of being hidden inside a polished final number.
Run one sensitivity test after the baseline answer.
Change the input most closely connected to cash-and-carry arbitrage, hold the remaining assumptions fixed and recompute only the affected steps. Explain whether the movement in continuous compounding matches the mechanism.
This cash-and-carry arbitrage sensitivity shows which assumption controls the conclusion and prevents a single scenario from being presented as universal.
Use a three-column cost of carry error log for fnce30007: translation error, calculation error and interpretation error.
Record the exact line where the cash-and-carry arbitrage solution first diverged, rewrite that line, and check it with a limiting case or an independent calculation.
Correcting the first failed cash-and-carry arbitrage move is more useful than copying the complete solution again.
Transfer to Forward and Futures Pricing
A complete response should make the task visible before the detail: identify what must be decided, define the relevant terms, connect the evidence to cash-and-carry arbitrage, and use continuous compounding to test the result.
The final sentence about continuous compounding should answer the question actually asked rather than merely repeat the topic.
The controlling limit is specific: Transaction costs, short-sale limits, stochastic rates and non-investment assets can create departures from the simple identity.
Keep that continuous compounding limit beside the worked example, because it separates a careful fnce30007 answer from one that sounds confident but claims more than the task or evidence supports.
For revision, retrieve cost of carry, cash-and-carry arbitrage and continuous compounding without notes, explain their relationship aloud, then complete a changed version of the application: derive forward or futures price from spot, rates and income.
Record the first failed cash-and-carry arbitrage reasoning move and repair it before attempting another case.
What this chapter covers
- 01
cost of carry
- 02
cash-and-carry arbitrage
- 03
continuous compounding
- 04
Applying cost of carry
- 05
Limits of cash-and-carry arbitrage and continuous compounding
Price an index future
- 1Identify S0, r, q and T.
- 1Use F0 = S0 exp((r-q)T).
- 1Calculate about 7,105.79.
- 1State the no-arbitrage assumptions.
Key terms
- cost of carry
- Net financing, storage, income and convenience effects of holding an underlying to maturity. This chapter uses the concept when students derive forward or futures price from spot, rates and income. Use this definition when the task is to derive forward or futures price from spot, rates and income.
- cash-and-carry arbitrage
- Trade combining spot financing and forward sale to exploit an overpriced forward under ideal assumptions. It helps explain the reasoning required to derive forward or futures price from spot, rates and income. Use this definition when the task is to derive forward or futures price from spot, rates and income.
- continuous compounding
- Interest convention in which value grows exponentially at a continuously compounded rate. Its limit matters because transaction costs, short-sale limits, stochastic rates and non-investment assets can create departures from the simple identity. Use this definition when the task is to derive forward or futures price from spot, rates and income.
Forward and Futures Pricing FAQ
What is the main task in Forward and Futures Pricing?
Derive forward or futures price from spot, rates and income.
How do cost of carry and cash-and-carry arbitrage work together?
Use cost of carry to establish the object or condition, then use cash-and-carry arbitrage to explain how it changes the outcome being analysed.
What must a fnce30007 answer qualify here?
Transaction costs, short-sale limits, stochastic rates and non-investment assets can create departures from the simple identity.
How should I revise Forward and Futures Pricing?
Retrieve cost of carry, cash-and-carry arbitrage and continuous compounding, apply them to a changed case, and correct the first point where the evidence no longer supports the conclusion.
Exam move
Reconstruct the relationship among cost of carry, cash-and-carry arbitrage and continuous compounding; complete the chapter application without notes; then test the result against this limit: Transaction costs, short-sale limits, stochastic rates and non-investment assets can create departures from the simple identity.
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