CFA Level I · CFA Level I Exam · Arbitrage, Replication, and the Cost of Carry in Pricing Derivatives
A stock is priced at $80. It will pay a $2 dividend in three months. The annual risk-free rate is 5% with continuous compounding. The no-arbitrage forward price for a 6-month contract is closest to:
The forward price is about $79.99. Compound the $80 spot price for six months at 5% to get roughly $82.03, then subtract the dividend's future value at contract expiry, about $2.03. Ignoring the dividend would wrongly give $82.03.
- A$78.00
- B$79.99Correct
- C$82.03
Explanation
Future value of spot: 80 × e^(0.025) = 80 × 1.025315 = 82.025. Future value of the dividend at month 6: 2 × e^(0.05×0.25) = 2 × 1.012578 = 2.025. F0 = 82.025 − 2.025 = 80.00, so about $79.99–$80.00. Ignoring the dividend gives $82.03.
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