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FRM Part I · FRM Exam Part I · Pricing Financial Forwards and Futures

A non-dividend-paying stock trades at USD 50. The continuously compounded risk-free rate is 4% per year. What is the no-arbitrage forward price for delivery in 6 months (approximately)?

The forward price is about USD 51.01. For a non-dividend-paying asset the forward equals spot compounded at the risk-free rate over the maturity: 50 × e^(0.04 × 0.5) = 51.01. Discounting or ignoring the half-year fraction gives incorrect values.

  1. AUSD 50.00
  2. BUSD 51.01Correct
  3. CUSD 52.04
  4. DUSD 49.01

Explanation

F0 = S0 e^(rT) = 50 × e^(0.04×0.5) = 50 × e^0.02 = 50 × 1.02020 = 51.01. Using the full annual rate without scaling by time gives 52.04, which is wrong because the maturity is only half a year. Discounting instead of compounding gives 49.01.

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