FRM Part I · FRM Exam Part I · Pricing Financial Forwards and Futures
A non-dividend-paying stock trades at $80. The continuously compounded risk-free rate is 5% per year. What is the no-arbitrage price of a 6-month forward contract on the stock?
The forward price is $82.02. With no income on the stock, the forward equals the spot price compounded at the risk-free rate: 80 × e^(0.05×0.5) = 82.02. Discounting or using the wrong time period gives incorrect values.
- A$82.02Correct
- B$84.00
- C$80.00
- D$78.02
Explanation
F0 = S0 e^(rT) = 80 × e^(0.05×0.5) = 80 × e^0.025 = 80 × 1.025315 = 82.025, about $82.02. The $84.00 option uses a full year of simple interest (80 × 1.05) instead of 6 months of continuous compounding. The $78.02 option discounts instead of compounding.
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