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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? (e^0.02 = 1.020201)

The forward price is about USD 51.01. With no income on the stock, the forward equals the spot price compounded at the risk-free rate for the contract life: 50 × e^(0.04×0.5) = 50 × 1.020201.

  1. AUSD 51.01Correct
  2. BUSD 52.00
  3. CUSD 50.00
  4. DUSD 49.01

Explanation

For an asset with no income, F0 = S0 e^(rT) = 50 × e^(0.04×0.5) = 50 × 1.020201 = 51.01. Using the simple rate gives USD 51.00, and ignoring the time value gives 50. Discounting instead of compounding gives about 49.01, which is wrong because the forward must include the cost of financing.

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