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FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage

A trader entered a long forward on a non-income-paying asset with delivery price K = USD 100. The spot price is now USD 105, 1 year remains to maturity, and the continuously compounded risk-free rate is 5%. What is the current value of the forward to the long position?

The forward is worth USD 9.88 to the long. Its value is the spot price minus the present value of the delivery price: 105 − 100 × e^(−0.05) = 105 − 95.12. Using the undiscounted gain of 5 or the undiscounted forward gap of 10.38 ignores discounting.

  1. AUSD 9.88Correct
  2. BUSD 5.00
  3. CUSD 10.38
  4. DUSD 0.13

Explanation

Value = S0 − K × e^(−rT) = 105 − 100 × e^(−0.05) = 105 − 95.12 = 9.88. USD 5.00 ignores discounting of K. USD 10.38 is F − K = 110.38 − 100 without discounting. USD 0.13 compares the new forward price of 110.38 with the wrong benchmark.

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