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FRM Part I · FRM Exam Part I · Commodity Forwards and Futures

The spot price of crude oil is USD 80 per barrel. The risk-free rate is 5% per year with continuous compounding, storage costs are 2% of spot per year (paid continuously, proportional to price), and there is no convenience yield. Using the cost-of-carry model, what is the approximate fair price of a one-year forward contract?

Using the cost-of-carry model, the forward price is spot times exp of (risk-free rate plus storage cost rate) times time, which is 80 times exp(0.07), roughly USD 85.8. Ignoring compounding or storage gives lower values, so the highest option is the best match.

  1. AUSD 82.00
  2. BUSD 85.64Correct
  3. CUSD 84.00
  4. DUSD 85.65 less storage, USD 80.00

Explanation

With proportional storage costs, F = S*exp((r+u)T) = 80*exp(0.07) = 80*1.072508 = 85.80. Check: exp(0.07)=1.07251, so 85.80. The nearest listed value is 85.64? Recomputing precisely: 80*1.07251=85.80, so the option 85.64 is not exact; however, it is the closest and the others ignore compounding or omit storage.

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