FRM Part I · FRM Exam Part I · Pricing Conventions, Discounting, and Arbitrage
A non-dividend-paying stock trades at USD 100. The continuously compounded risk-free rate is 5% per year. What is the no-arbitrage price of a one-year forward contract on the stock?
The forward price is USD 105.13. With no income on the asset, the forward equals spot compounded at the risk-free rate, 100 × e^0.05. Discounting instead of compounding, or using simple interest, gives wrong values.
- AUSD 105.13Correct
- BUSD 105.00
- CUSD 100.00
- DUSD 95.12
Explanation
With no income and no storage costs, F = S0 × e^(rT) = 100 × e^0.05 = 105.13. USD 105.00 uses simple interest rather than continuous compounding. USD 95.12 discounts the spot price instead of compounding it forward.
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